Before revision: The foldability of rigid origami has been widely studied and applied to many engineering fields. In this article we introduce the statics of rigid origami, find the form of stress and load, and prove the equivalence of static rigidity and  first-order rigidity.
After revision: Rigid origami is examined from the perspective of rigidity theory. First and second order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and first-order rigidity.