Shark Fin Sales Elimination Act of 20 21 This bill makes it illegal to possess, buy, sell, or transport shark fins or any product containing shark fins, except for certain dogfish fins. A person may possess a shark fin that was lawfully taken consistent with a license or permit under certain circumstances. Penalties are imposed for violations under the Magnuson-Stevens Fishery Conservation and Management Act. The maximum civil penalty for each violation shall be $100,000, or the fair market value of the shark fins involved, whichever is greater.