Abstract Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-ratetensor. However, the Jaumann-stress rate is known to display spuriousnon-physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow intensile deformation. In this paper a ’’compressible-Leonov model‘‘ is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric deformation. This has the advantage that the model can be extended in a straightforward way to include aspectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in ahomogeneous uniaxial tensile test and a homogeneous plane-stress sheartest, using polycarbonate (PC) as a model system. All models considered in this paper are ’’single mode‘‘ models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, northe strain-hardening or strain-softening response.