The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate are derived from Hellinger-Reissner's variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions.  Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations.