Traditionally, origami-based structures are designed on the premise of "rigid folding," meaning that the facets and fold lines of origami can be replaced with rigid panels and ideal hinges, respectively. Rigid folding is an important factor in defining origami for mathematicians and geometricians. However, ideal rigid folding is impossible in real structures and every act of folding and unfolding is accompanied by elastic deformations. In this study, we focus on these elastic deformations in order to expand origami into a new method of designing morphing structures. We start by proposing a simple model for evaluating elastic deformation in nonrigid origami structures. In this model, the facets of origami are replaced with plates that are not only rigid but also elastic. This partially elastic origami model has a one-degree-of-freedom mechanism; therefore, its folding process can be described using rigid folding simulation techniques. In this process, the deformations of the elastic plates can be calculated and we can estimate the elastic energy through folding/unfolding. We then apply these methods to deployable plate models constructed of quadrilateral plates and hinges to design new deployable structures. Initial strain is introduced into the elastic parts of the partially elastic origami model and these parts function as actuators for deployment. Then, by using the finite element method, we conduct numerical simulations and confirm the deploying capabilities of the models.