At present, powder metallurgy is becoming more and more widespread due to the construction of large gasostatic extruders, which make it possible to produce a wide range of products of large geometric dimensions with high performance characteristics. In this paper, we investigate the effect of viscosity on the process of hot isostatic pressing of a long cylindrical billet, which is one of the typical problems solved in production. The insistence of the problem is due to the peculiarities of the hot isostatic compaction process, associated with significant distortions in the shape of the product during the process, as well as the high complexity and cost of further processing. Also, because of the high cost of raw materials, carrying out field experiments is seriously hampered. Under these conditions, it is important to consider all the factors affecting the final form of the product, one of which is the dependence of the yield stress on the strain rate intensity, which is assumed to be given in power form in the work. Powder material in the work is considered as a single plastically compressible medium under conditions of an inhomogeneous non-stationary temperature field. A general formulation is considered that includes the equilibrium equation, the fluidity equation, the associated flow law, the ideal plasticity condition and the incompressibility condition, the continuity equation. The problem of hot isostatic pressing of a long cylindrical billet, which is a capsule with a powder material placed in it, is also considered. The influence of the capsule on the ends of the cylinder is neglected. In this formulation, the Green’s fluidity condition is used to describe the mechanical properties of the powder material. Relations are obtained that make it possible to evaluate the qualitative picture of the processes occurring at different stages of the hot isostatic pressing process (HIP). Calculations are made for the ratio of the initial cylinder sizes to the final ones, depending on the parameters.