Gas Price and Refinery Capacity Relief Act of 2013 - Amends the Energy Independence and Security Act of 2007 to require a refinery owner or operator to report to the Administrator of the Energy Information Administration (EIA): (1) at least one year in advance the schedule for any planned removal from service for maintenance, repair, or modification of any refinery or a unit (planned refinery outage); and (2) as soon as practicable any unplanned refinery outages.

Directs the Secretary of Energy to: (1) review, analyze, and make available to refinery operators information on unplanned refinery outages in order to prevent significant market disruptions; and (2) analyze the costs and benefits of creating a national strategic refined petroleum products reserve for refined petroleum products.