Closed upsetting is the first step of steel pipe vertical extrusion technology. In this paper, the closed upsetting process was investigated by upper bound method, slip-line field and thermo-mechanical coupled FEM based on Deform 2D. The flow behavior, effective strain, temperature field and upsetting load were examined. The influence of billet temperature and die velocity on filling factor and upsetting load was discussed. The error percentage of upsetting load computed by upper bound method and FEM was less than ±1%. Simulation results showed that the closed upsetting process of P91 was more sensitive to temperature, while the impact of velocity was not as significant as temperature.