Abstract: Based on Hamilton variation principle,the equations of motion for the moderately thick rectangular plate with transverse surface penetrating crack on two-parameter foundation are established.The transverse shear deformation and the coupled effect of the foundation are taken into account.The deflection functions satisfying all boundary conditions and the crack's conditions are proposed and the equations are solved using Galerkin method.In numerical computations,the effect of the crack location and depth on the vibration behavior of the moderately thick rectangular plates with free boundary is considered.