In this article, we model the mechanical behavior of light-activated shape memory polymers with a view toward determining the effect of the viscoelasticity of the polymers with regard to their shape memory response. This study is a companion to our earlier investigation of both isotropic and anisotropic elastic light-activated shape memory polymers. The constitutive model is based on a multi-network approach consisting of two microstructural networks, the original network and the second network that is formed due to light irradiation. A single integral model is adopted to incorporate the viscoelastic response in the original and second networks. We study the response of viscoelastic light-activated shape memory polymers subject to uniaxial and biaxial tension. Parametric studies are carried out to obtain a better understanding of the effect of quantities such as relaxation time and the ratio of the relaxation modulus to the instantaneous modulus. A combination of the classical trapezoidal integration method, recursive scheme, and root-finding methods is adopted to solve the governing equations. Finally, the model is used to describe the stress relaxation behavior of light-activated shape memory polymer reported in the literature.