UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the

Securities Exchange Act of 1934

Filed by the Registrant  x                             Filed by a Party other than the Registrant  ¨

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¨ Preliminary Proxy Statement

¨ Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

¨ Definitive Proxy Statement

¨ Definitive Additional Materials

x Soliciting Material Under Rule 14a-12

Carmike Cinemas, Inc.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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EXPLANATORY NOTE

On June 21, 2016, Carmike Cinemas, Inc. (“Carmike” or the “Company”) issued the following document in connection with proxy advisory reports issued by Institutional Shareholder Services Inc. and Glass, Lewis & Co., LLC.

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Carmike Cinemas, Inc. Additional Information Regarding Stockholder Solicitation

Contrary to the claims of ISS, Glass Lewis, Mittleman and Driehaus, AMC’s $30 per share cash offer reflects fair value for Carmike’s stockholders.

ISS ignores several important factors when concluding that “it would not be such a stretch…to achieve [a $30 per share valuation] on a standalone basis.”

• Despite recognizing that fundamental economic differences in Carmike’s rural theatre footprint have resulted in the Company persistently trading at a discount relative to its peers, ISS wrongly “assumes away” the implications and likelihood that the trading discount will continue.

^¡  Relative to its competitors, Carmike has:

¡ Smaller scale and financial capacity to invest in theatre upgrades

¡ Lower EBITDA / operating margins

¡ Lower per-screen financial metrics

¡ No regular dividends

• ISS fails to appreciate the role of new acquisitions in Carmike’s growth strategy, and the challenges the Company faces as the pace of our acquisition activity has slowed to a point well below historical levels and our previous expectations, despite our intense focus on sourcing new targets. Furthermore, Carmike must compete with its larger, better capitalized peers to acquire attractive tuck-in targets.

• ISS does not appreciate that Carmike has no control or influence over some key business drivers, including box office performance, where recent published reports have suggested a soft second calendar quarter with negative implications for the balance of 2016.

• ISS’s conclusion conflicts with its own acknowledgement that the $30 per share offer price was “in line” or “above” 8 of the 9 metrics in J.P. Morgan’s fairness opinion analysis, and that the only metric “below” the offer price incorporated the speculative benefit in 2017 of acquisitions not yet executed or even identified by Carmike.

• ISS’s analysis wrongly relies on the fact that Carmike stock traded above $30 for “18% of the total trading days leading up to the transaction announcement” – but fails to recognize that the stock last traded above $30 per share on May 6, 2015, and prior to that time had been affected by public reports of a potential sale.

• ISS states that “Carmike’s EV/FY2017 EBITDA multiple at the offer price is only 7.1x, or basically in line with the company’s median standalone multiple over the one-year period prior to announcement,” without recognizing that it is inappropriate to compare a two-year forward multiple with a “next-twelve-months” multiple to assess valuation.

• Finally, ISS fails to appreciate that achieving a sustainable $30 per share public trading valuation as a standalone, smaller company in a volatile industry facing secular headwinds and challenged growth strategy is a much riskier proposition than providing full liquidity for Carmike stockholders at $30 per share through a sale of the company.

When analyzed properly, the transaction valuation for Carmike’s stockholders is compelling.

• Although ISS contends that Carmike has “scarcity value” as an acquisition target, the facts show that no other buyer has emerged with a transaction proposal, despite the fact that the board has conducted multiple market checks since December 2014 and there has been public speculation about a potential sale since at least March 2015.

• The notion that the sharing of synergies is “inequitable” rests entirely on the date used to measure AMC’s stock price. For instance, using AMC’s closing price as of June 17th, Driehaus’ methodology would imply that Carmike stockholders capture approximately 50% of the synergies from the $30 per share deal price. Incidentally, this also demonstrates the value to Carmike stockholders of the certainty provided by an all-cash offer.

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• The $126mm of adjusted 2015 EBITDA used to calculate our estimated transaction multiple of 8.8x FV/LTM EBITDA reflects the substantial expenses we must incur on an ongoing basis to execute our acquisition strategy and provide competitive compensation to management, and is therefore the appropriate basis for evaluating a transaction valuation.

• In addition, ISS failed to analyze any precedent M&A transactions, and ignored our own presentation addressing this important point, which highlighted that our estimated transaction multiple of 8.8x FV/LTM EBITDA is the highest multiple paid for a large-scale theatre transaction in a decade.

• Contrary to Mittleman and Driehaus’ claims, we accounted for the value of Screenvision to Carmike when assessing the proposed transaction with AMC. In addition, AMC has informed Carmike that it will be subject to “make-good” payments and tax liabilities from “founder’s unit grants” that will likely materially offset any benefit it derives from owning Screenvision. Furthermore, both Mittleman and Driehaus’ analysis failed to acknowledge the cost to achieve any operational synergies.

• Our valuation also accounted for the benefits we derive from our net operating losses. As we have publicly disclosed previously, the value is limited for Carmike due to existing Section 382 limitations. In addition, we believe the benefits potentially would be further limited for an acquirer in a change-of-control transaction.

Disclosure Regarding Forward-Looking Statements

This communication contains forward-looking statements within the meaning of the federal securities laws. Statements that are not historical facts, including statements about the Company’s beliefs, expectations and future performance, are forward-looking statements. Forward-looking statements include statements preceded by, followed by or that include the words, “believes,” “expects,” “anticipates,” “plans,” “estimates,” “seeks” or similar expressions. Forward-looking statements are only predictions and are not guarantees of performance. These statements are based on beliefs and assumptions of the Company’s management, which in turn are based on currently available information. The forward-looking statements also involve risks and uncertainties, which could cause actual results to differ materially from those contained in any forward-looking statement. Many of these factors are beyond the Company’s ability to control or predict. Important factors that could cause actual results to differ materially from those contained in any forward-looking statement include, but are not limited to: the occurrence of any event, change or other circumstances that could give rise to the termination of the merger agreement with AMC Entertainment Holdings, Inc. (“AMC”); the inability to complete the proposed merger due to the failure to obtain the Company stockholder or regulatory approval for the proposed merger or the failure to satisfy other conditions of the proposed merger within the proposed timeframe or at all; disruption in key business activities or any impact on the Company’s relationships with third parties as a result of the announcement of the proposed merger; the failure to obtain the necessary financing arrangements as set forth in the debt commitment letters delivered pursuant to the merger agreement with AMC, or the failure of the proposed merger to close for any other reason; risks related to disruption of management’s attention from the Company’s ongoing business operations due to the proposed merger; the outcome of any legal proceedings, regulatory proceedings or enforcement matters that may be instituted against the Company and others relating to the merger agreement with AMC; the risk that the pendency of the proposed merger disrupts current plans and operations and the potential difficulties in employee retention as a result of the pendency of the proposed merger; the amount of the costs, fees, expenses and charges related to the proposed merger; adverse regulatory decisions; unanticipated changes in the markets for the Company’s business segments; general economic conditions in the Company’s regional and national markets; the Company’s ability to comply with covenants contained in the agreements governing the Company’s indebtedness; the Company’s ability to operate at expected

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levels of cash flow; financial market conditions including, but not limited to, changes in interest rates and the availability and cost of capital; the Company’s ability to meet its contractual obligations, including all outstanding financing commitments; the availability of suitable motion pictures for exhibition in the Company’s markets; competition in the Company’s markets; competition with other forms of entertainment; the effect of the Company’s leverage on its financial condition; prices and availability of operating supplies; the impact of continued cost control procedures on operating results; the impact of asset impairments; the impact of terrorist acts; changes in tax laws, regulations and rates; and financial, legal, tax, regulatory, legislative or accounting changes or actions that may affect the overall performance of the Company’s business.

Consider these factors carefully in evaluating the forward-looking statements. Additional factors that may cause results to differ materially from those described in the forward-looking statements are set forth in the Company’s Annual Report on Form 10-K for the fiscal year ended December 31, 2015, which was filed with the U.S. Securities and Exchange Commission (the “SEC”) on February 29, 2016, under the heading “Item 1A. Risk Factors,” and in its subsequently filed reports with the SEC, including Forms 10-Q and 8-K. Readers are cautioned not to place undue reliance on the forward-looking statements included in this presentation, which speak only as of the date hereof. The Company does not undertake to update any of these statements in light of new information or future events, except as required by applicable law.

Important Additional Information Regarding the Merger

This communication may be deemed to be solicitation material in respect of the proposed merger of the Company with and into a wholly-owned subsidiary of AMC. In connection with the proposed merger, the Company filed a definitive proxy statement with the SEC on May 23, 2016. The Company mailed the definitive proxy statement to its stockholders on or about May 25, 2016. BEFORE MAKING ANY VOTING DECISION, THE COMPANY’S STOCKHOLDERS ARE URGED TO READ THE DEFINITIVE PROXY STATEMENT IN ITS ENTIRETY AND ANY OTHER DOCUMENTS TO BE FILED WITH THE SEC IN CONNECTION WITH THE PROPOSED MERGER OR INCORPORATED BY REFERENCE IN THE DEFINITIVE PROXY STATEMENT BECAUSE THEY WILL CONTAIN IMPORTANT INFORMATION ABOUT THE PROPOSED MERGER.

The Company’s stockholders are able to obtain a free copy of the definitive proxy statement and other relevant documents filed by the Company with the SEC at the SEC’s website at www.sec.gov. In addition, the Company’s stockholders may obtain a free copy of the proxy statement and other relevant documents from the Company’s website at http://www.carmikeinvestors.com/.

Participation in the Solicitation

The Company and its directors, executive officers and certain other members of management and employees of the Company may be deemed to be “participants” in the solicitation of proxies from the Company’s stockholders in connection with the proposed merger. Information regarding the interests of the persons who may, under the rules of the SEC, be considered participants in the solicitation of the Company’s stockholders in connection with the proposed merger, which may be different than those of the Company’s stockholders generally, is set forth in the definitive proxy statement filed with the SEC on May 23, 2016. The Company’s stockholders may obtain a free copy of the definitive proxy statement from the Company in the manner set forth above.