Research works involving structural origami have grown in recent years, especially applied to science and engineering problems. Early applications took advantage of the idea that a system can be folded compactly and subsequently deployed, and that self-assembly can be used to construct a three dimensional structure by starting from a thin sheet. The present work compares bar and hinge models with the simplest hybrid finite element models for plate and shell in order to represent origami structure panels. The hybrid finite element formulation is based on the Hellinger-Reissner potential for an approximation of the stress field, thus satisfying the equilibrium equation of the elasticity problem in the domain. The bar and hinge model approach, as given in the literature, is based on folded patterns as pin-jointed truss frameworks. Each vertex in the folded sheet is represented by a pin-joint, and every fold line by a bar element. Numerical examples show the mechanical behavior of these structures and the folding energy using eigenvalues of the respective eigenmodes. Dynamic analysis of the models is also carried out for structure assemblages with one, two and four cells.