Origami structures exhibit desirable stowage properties for application in deployable space structures. This work presents a description of the kinematics and proposes a design method using topology optimization. In order to expand the design envelope, using a truss model, the objective is to find the optimal configuration of the trusses based on axial rigidity and the crease pattern that maximizes the displacement at set locations, under prescribed forces and boundary conditions. First, a linear method is used to determine small strain and small rotation mechanics of flexible origami, with the aim of studying the behavior at the initiation of folding. Subsequently, a nonlinear method is implemented to consider large displacement and large rotation mechanics.