Based on Reissner plate theory and using Hamilton variational principle, the nonlinear equations of motion are derived for the moderate thickness rectangular plates with transverse surface penetrating crack on an elastic foundation under the action of periodic load. The suitable expressions of trial functions satisfied all boundary conditions and crack’s continuous conditions are proposed. By using the Galerkin method and the Runge-Kutta integration method, the nonlinear equations are solved. The possible bifurcation and chaos of the system are analyzed under the action of external load. In numerical calculation, the influences of the different location and depth of crack and external load on the bifurcation and chaos of the rectangular moderate thickness plates with freely supported boundary are discussed.