One purpose of the present invention is to provide an epoxy resin composition which is for obtaining a fiber-reinforced composite material that combines heat resistance with tensile strength on a high level. The other purpose is to provide: a fiber-reinforced composite material obtained using this epoxy resin composition; and a molded article and a pressure vessel both containing the fiber-reinforced composite material. The present invention has the following configuration in order to achieve the above purposes. Namely, the epoxy resin composition includes the constituent element [A]: An epoxy resin including an aromatic ring and having a functionality of 2 or higher and the following constituent element [B]: An amine-based hardener or an acid anhydride-based hardener, and is characterized in that a cured object obtained by curing the epoxy resin composition has a rubber-state modulus of 10 MPa or less when evaluated for dynamic viscoelasticity and the cured object has a glass transition temperature of 95° C. or higher.