The so-called smart structures are frequently inspired by the art of origami, and they are in many cases considered to be manufactured of smart materials such as shape memory materials. We propose a mathematical model for such origami-like structures made of light activated shape memory polymers, and we develop a reference code for computer simulations of such structures. The proposed mathematical model is based on an existing macroscopic phenomenological model by (Sodhi & Rao 2010, Int. J. Eng. Sci. 48, 1576), which has been developed in order to describe full three-dimensional deformation of light activated shape memory polymers. This model is suitably modified for the reduced representation of origami-like structures which is based on the bar-and-hinge approach. The numerical solution of the corresponding governing equations is implemented using a transparent modification of a state-of-the-art code for numerical simulation of purely elastic origami-like structures developed by (Liu & Paulino 2017, Proc. R. Soc. A: Math. Phys. Eng. Sci. 473, 20170348).