A 3D thermoviscoelastic model is proposed to represent the thermomechanical behavior of shape memory polymers. The model is based on a physical understanding of the material behavior and a mechanical interpretation of the stress–strain–temperature changes observed during thermomechanical loading. The model is thermodynamically motivated and is formulated in a finite strain framework in order to account for large strain deformations. Model predictions capture critical features of shape memory polymer deformation and, in some cases, provide very favorable comparisons with experimental results. POLYM. ENG. SCI. 46:486–492, 2006. © 2006 Society of Plastics Engineers.