An algorithm for unconditionally stable and accurate integration of elasto-viscoplastic pressure-dependent constitutive model is presented. Rate form constitutive equations of thermal-elastoviscoplastic type with compressibility take into account the changes in relative density. The algorithm computes the deviatoric and volumetric creep strains by finding the value of the effective stress which satisfies the functional relationship, the effective stress function. Thus, one non-linear scalar equation is solved to find the unknown volumetric and deviatoric components of creep strain tensor. The tangent modulus is evaluated consistent with the integration algorithm. The application of the method to the simulation of hot isostatic pressing of metal powder is shown. The paper presents the solution of the verification problem and comparison with the experimental result.