The paper deals with the influence of viscous creep of steel on the behaviour of steel structures during fire. Two stress-strain relationships for structural steel, combined with Harmathy's explicit model of viscous creep at elevated temperatures, are presented in the paper: (i) bilinear stress-strain relationship and (ii) modified Poh's stress-strain relationship. The presented models have been implemented in self-developed software Pozar for numerical analysis of mechanical response of planar steel frames in fire. Further on results are validated against experimental ones published by Rubert and Schaumann, 1985. The numerical results, obtained with stress-strain relationship according to the Eurocode 3, are added for comparison. It is shown that all tested models give satisfactory results for small load ratios. Poh's stress-strain relationship in combination with Harmathy's model of viscous creep and newly proposed coefficients give the best results among the tested models with explicitly considered viscous creep. However, none of the considered models give good agreement with the experiment at high values of load ratio. Furthermore, the comparison between the different material and creep models is conducted for three heating regimes, namely linear heating regime and fast and slow natural fire development. A prominent influence of the employed material model on the final midspan displacements is observed.