Constitutive relations are derived for viscoelastic polymers. These relations are applicable to polymers for temperatures above their glass transition temperature and strain rates ranging from quasistatic up to shock regimes. Linear viscoelasticity is assumed for small tensile deformations but nonlinear effects, arising from void growth, become important at larger strains. Our void growth model is based on a generalization of Eshelby’s Green’s function solution to the problem of an ellipsoidal void in an elastic material. We apply our analysis to study the mechanical properties of polyvinyl acetate under dynamic loading conditions. Void concentration and aspect ratio considerations are found to be important in general deformation events. Uniaxial tension tends to favor aspect ratio change, while non-spherical voids are observed to evolve into spherical ones as tensile strain approaches triaxiality. [Research supported by the USDOE under contract W-7405-ENG-36]