The finite element method of structural analysis is extended to the problem of stability of plates. Stability coefficient matrices are derived for rectangular plates for constant and variable direct stresses and shear stresses. These, in conjunction with the stiffness matrix, allow an easy modification of the conventional plate stiffness matrix to include the effects of in-plane stresses, thus giving a simple and rapid formulation of stability problems for plates. The method is applicable to a wide variety of problems. This includes plates with variable moment of inertia, anisotropic plates, plates with any type of edge or body loadings, plates subjected to thermal stresses and plates coupled with other elements such as beams, ribs, etc., with all types of boundary conditions.