Abstract Small punch creep tests on Type 304 stainless steel have been performed at 650 °C. Based on these tests, a finite element model, with modified Kachanov–Rabotnov creep damage constitutive equations, was established. The variation of central deflection and creep strain with time and the evolution of creep damage under constant loads were analysed by using the finite element model. The central creep deflection curves in the specimens were obtained at different loads in both tests and simulations and have three different stages, similar to conventional creep tests. There is good agreement between experimental results and simulation data. The creep damage at the central part is high, and localization of damage is obvious. Initial failure occurs at the bottom surface, about 0.8 mm away from the centre which agrees well with the finite element mode observation.