Hybrid power plants consisting of a solid oxide fuel cell (SOFC) and a gas turbine show high electrical efficiencies, however require pressurisation of the SOFC to several bar. This paper presents a theoretical investigation of the pressure influence on SOFC performance and durability. A two‐dimensional elementary kinetic model is used to predict the performance of a single cell in the pressure range of 1–20 bar. The influence of pressure on thermodynamics, reaction kinetics, porous electrode diffusion, channel transport and efficiency is assessed. It was found that polarisation resistance decreases with increasing pressure due to increased diffusion through porous electrodes and a higher electrode surface coverage with reactant species. Furthermore, open‐circuit voltage increases slightly with pressure. As a consequence, power density and efficiency increase upon pressurisation with the strongest increase at low pressures between 1 and 5 bar. The influence of pressure on two typical degradation mechanisms, nickel oxidation and carbon deposition, is assessed using thermodynamic simulations. Pressurisation facilitates nickel oxidation whereas its effect on carbon deposition strongly depends on temperature.