A nonlinear viscoelastic model is described that can predict the time-dependent deformation of a polymer under a multiaxial stress. The main material property requirements are tensile creep compliances over a suitable time range and at different stress levels over which creep behavior is nonlinear. Some creep data under uniaxial compression are also required. Relationships are derived between multiaxial stress and strain components for arbitrary stress or strain histories. The model has been coded into a finite element system to enable stress analyses to be carried out on objects of complex geometry. The validity of the model is explored through comparisons of predicted and measured results from a test that is designed to produce a predominantly shear stress state in the gauge region of the specimen. Results are presented for loadings under constant stress and constant deformation rate. POLYM. ENG. SCI., 51:2210-2219, 2011. (C) 2011 Society of Plastics Engineers