The effect of the transverse shear deformation for Reddy plates or laminated plates is significant. In this case,it can meet the requirements for calculate precision better to use the third order shear deformable theory than to use the classical thin plate theory and the first order shear deformation theory. And it is better to describe the distribution of the plate shear deformation and shear stress varying through the thickness when using the third order shear deformation theory. In this paper,an analytical method is presented for studying the free vibration characteristic of plate using the third order shear deformation theory on different boundary conditions,which are the any combinations of simply supported,free and clamped. Hamilton principle is used to formulate the free vibration equations. Then,by introducing the intermediate variable the original coupling free vibration equations are decoupled and simplified. The fundamental function expressions are obtained basing on the method of separation of variables and the boundary conditions. And the natural frequencies and modal functions are obtained by using the Rayleigh-Ritz method. The method in this paper has a good generality for solving the vibration problems of thick plates under different boundary conditions. The result obtained in this paper can provide a theoretical basis for thick plate's application in engineering,and it has relatively high application value.