The production method according to the present disclosure comprises obtaining a product containing the fluoroethane from a fluoroethylene by a reaction in the presence of catalysts. Each catalyst is formed by supporting a noble metal on a carrier. A reactor for performing the reaction is filled with a catalyst having a noble metal concentration of C1 mass % based on the entire catalyst and a catalyst having a noble metal concentration of C2 mass % based on the entire catalyst to form an upstream portion and a downstream portion, respectively; and C1