A nonlinear viscoelastic constitutive model, in differential form, is presented based on the deformation characteristics of thermoset polymers under complex loadings. This rheological model includes a criterion to delineate loading and unloading in multiaxial stress states, and different moduli for loading and unloading behaviors. The material constants and functions of this model are calibrated in accordance with a well-defined procedure. The model predictions are compared with the experimental data of an epoxy polymer subjected to uniaxial and biaxial stress states with monotonic and cyclic loading. The agreement is very good for various loading regimes. The constitutive model is further implemented in a finite element code and the residual stresses arising from the curing process of polymer reinforced composites is determined for two different epoxy resins.