Eliminating Profiteering Through Illegal Cigarette Sales Act or EPICS Act - Prohibits the sale of tobacco products advertised through the Internet or other means to an individual under the legal age when such products are shipped by carrier in or affecting interstate commerce and the seller fails to comply with each of specified procedures. Includes in such procedures receiving a copy of a government-issued document providing the identity, address, and birth date of the buyer and a signed statement of certain confirmations of an order before any such products are so shipped.

Requires tobacco product advertising on the Internet to prominently display a warning label unless cigarettes are being sold to someone in the business of selling tobacco products. Deems violations of provisions of this Act regarding unlawful sales to minors to be unfair or deceptive acts or practices in or affecting commerce under the Federal Trade Commission Act, and imposes criminal penalties.

Authorizes a State attorney general and certain other persons to bring a civil action for injunctive relief to restrain a person from engaging, or continuing to engage, in a violation of provisions regarding unlawful sales to minors.

Requires a person taking a delivery sale of cigarettes to include a certain statement regarding taxes in a conspicuous manner. Imposes penalties for certain offenses in delivering cigarettes, including for failure to abide by excise and sales tax laws of States.

Permits a State attorney general and certain other persons to bring an action in U.S. District Court to prevent and restrain violations of this Act.

Classifies cigarettes as nonmailable.

Modifies penal provisions regarding trafficking in contraband cigarettes.