Shape memory polymers (SMP's) are polymers that have the ability to retain a temporary shape, which can revert back to the original shape on exposure to specific triggers such as increase in temperature or exposure to light at specific wavelengths. A new type of shape memory polymer, light activated shape memory polymers (LASMP's) have been developed in the past few years. In these polymers the temporary shapes are fixed by exposure to light at a specific wavelength. Exposure to light at this wavelength causes the photosensitive molecules, which are grafted on to the polymer chains, to form covalent bonds. These covalent bonds are responsible for the temporary shape and act as crosslinks. On exposure to light at a different wavelength these bonds are cleaved and the material can revert back to its original shape. A constitutive model of LASMP's which based on the notion of multiple natural configurations has been developed (see Sodhi and Rao). In this work we use this model to analyze the mechanical behavior of LASMP's under a specific boundary value problem, namely, the problem of circular shear. We use this model problem to study the behavior of the LASMP's when a temporary configuration is formed by exposing the polymer to light. In addition we show that these materials are able to undergo complex cycles of deformation due to the flexibility with which these temporary configurations can be formed and removed by exposure to light.