Abstract: As one kind of deployable structures, foldable structures are widely used lately. The foldable structure is classified into the rigid foldable structure and the flexible foldable structure. The Singular Value Decomposition (SVD) method for the equilibrium matrix is developed and a physical explanation is given. With this method the structural analysis of static and kinematic indeterminate foldable systems is conducted and the kinematic bifurcation points of pin-connected foldable structures along motion paths are determined. The high level compatibility equation of pin-connected foldable structures is analyzed by this method. As examples, numerical analyses have been conducted on the cantilever and arch foldable structures as well as the foldable structure pin-connected with three bars.