The paper introduces a three-dimensional constitutive model for the mechanical behavior of amorphous polymers, thermosets and thermoplastics. The approach is formulated in terms of finite deformations, appropriate for glassy polymers. The rheology of the model consists of a Langevin-type free energy function for the energy storage due to molecular alignment connected in parallel to a Maxwell element with a viscoplastic dashpot. The model proves successful for the constitutive description of glassy polymers over a large range of strain rates. To capture the smooth softening behavior upon yielding is the main purpose of this research. It is reached under consideration of absolute temperature and current strain rate with the proposed evolution law for the viscoplastic dashpot deformation. The rate-dependence of amorphous polymers is reproduced as well as the pressure dependence during different loading scenarios. A fully implicit numerical scheme appropriate for the finite element implementation is presented. The modeling capability of the proposed approach is demonstrated for epoxy. PC and PMMA. The efficiency of the proposed numerical scheme is demonstrated via a necking simulation of a flat PC coupon. (C) 2012 Elsevier Ltd. All rights reserved.