Before revision:  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. Another concept introduced here is the pre-stress stability . We concern what is the stability of a creased paper when it is rigid but not statically rigid and how would the pre-stress contribute to the stability. The answer to these questions is also linked with the second-order rigidity. A brief discussion on the numerical methods to determine these rigidity concludes the article .
After revision:  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 or static rigidity implies prestress stability, which implies second-order rigidity, which implies rigidity, but none of these is reversible. Examples are given of rigid origami structures with these different kinds of rigidity. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required .