This paper is aimed to develop a model for the analytical description of the effect of direct current (DC) upon the steady-state creep of metals. For the mathematical apparatus, the synthetic theory of irrecoverable deformation is taken. As a result, relationships between creep rate, stress, temperature, and current intensity have been derived. For this purpose, a term, taking into account the passing of DC, is entered into the constitutive equation of the theory. The model results fit well experimental data. The analysis of loading surface in steady-state creep for the ordinary loading and that coupled with DC is provided.