This thesis deals with the influence of viscous creep of steel at elevated temperatures on the behavior of steel structure during fire. Models of viscous creep of steel at elevated temperatures are being extensively presented. For Harmathy's model of viscous creep of steel and bilinear material model of steel, new values of material parameters for Harmathy model were proposed for structural steel grade S355, based on experimental results of tensile bar. Similarly, for Harmathy's model of viscous creep of steel and modified Poh material model of steel, new values of material parameters were proposed for structural steel grade S355. Modified Poh material model was additionaly built into the program POZAR. The program is also complemented by a modified incremental–iterational process, which significantly increases the speed of computational analysis. In case of fire analysis of simply supported beam at 50 % of critical load, the computational analysis, with usage of modified algorithm, ends at least 57 times faster. The proposed values of material parameters for Harmathy viscous creep model at elevated temperatures were validated. Comparison between experimental and numerical results which were determined with proposed material parameters for Harmathy viscous creep model shows good agreement between the results only at low stress values. Accurate parametric analysis shows that the critical times of the typical steel frame for proposed values of material parameters for Harmathy viscous creep model are comparable. This applies to both the standard fire curve, as well as natural fire with fast and slow temperature increase in the fire area. The only difference is the deformability of frames, due to the model proposed by standard SIST EN 1993-1-2 being significantly stiffer.