The experimental studies of elasto-plastic deformation of tubular steel samples under proportional and non-proportional (monotonic and cyclic) loadings, including partial and intermediate loadings, have been conducted with the aim of improving the accuracy of the description of the complex passive loading processes. The plastic strain accumulation was observed in the course of tests carried out under passive loading. However, this effect turned out not to be described by the plastic flow theory. This result required the development of an alternative material model. The comparisons of experimental results with the predictions of the structural (rheological) elasto-plastic model and the multisurface theory of plasticity with one active surface were made. Modifications of the constitutive equations were proposed in order to improve the accuracy of the material response prediction.