Shape memory polymer (SMPs) are a class of smart materials that have the ability to retain multiple temporary shapes and recover original shapes as they exhibit deformation in response to external stimuli. The shape change in these polymers can be triggered using different stimuli like temperature, light, water, pH, magnetism, and their mechanisms can be easily altered. SMPs are capable of displaying multiple temporary and one permanent shape by either creating a multiphase system or by undergoing a very broad thermal transition. SMPs and their composites are also easy to manufacture, and complex structures can be 3D printed with multimaterials by controlling various geometric parameters. Their applications are diverse and found in various fields such as transportation, energy generation, deployable structures, clothing, healthcare, etc. It is therefore important to model the behavior of such a material. This work discusses the behavior of a thermally activated subclass of SMPs in which the temporary shape is fixed by a crystalline phase and a light activated subclass of SMPs in which the temporary shape is fixed by photo-reversible covalent crosslinks. Light activated SMPs (LASMPs) ease the temperature limitations faced by thermally activated SMPs while making remote activation possible, which opens an even wider range of applications. The thermo-mechanical behavior of such copolymers is simulated using a framework based on the theory of multiple natural configurations while incorporating the viscoelastic effects in a rate type model. The model is applied to different boundary value problems related to homogeneous deformations such as uniaxial extension of dual and triple shape memory polymers under controlled stress and strain conditions. The results are consistent with experimental observations and show how the complicated thermo-mechanical behavior and shape memory effect (SME) are influenced by parameters like temperature, external stress, crystallinity and bond formation.