This article shows the results of finite element analyses of small punch creep testing of a P91 steel at 600 °C using two different approaches to model the friction between the specimen and the punch. The numerical results obtained using the ‘classical’ Coulomb friction model (i.e. constant friction coefficient) have been compared with those obtained by a more modern formulation, which takes into account the effects of local loading conditions, that is, the contact pressure, between the contacting bodies (the small disc specimen and the punch) on the coefficient of friction. The aim of the work is to investigate the effects of the friction formulation used for the calculations on the numerical results representing the output of the test, that is, the variation of the punch displacement versus time and the time to rupture. The calculations, carried out for various load levels, showed that the friction coefficient is not constant at all positions on the contacting surface between the punch and the specimen during the deformation process. The maximum value for the coefficient of friction is reached at the contact edge, which is a very important region in the specimen, because this is the position at which most of the creep deformation occurs. As expected, the displacement versus time curve (that is usually the only output obtained from experimental small punch creep testing) is affected by friction formulation which is used, as this directly influences the stress and strain fields in the specimen.