Abstract: Based on the Refs.1-3, boundary displacement functions are treated as state variables and introduced into the state equation. The exact solutions are presented for the rectangular thick single and laminated plates with clamped edges. In the solving process, the state equation becomes a homogeneous equation from a nonhomogeneous one and the intermediate process to solve undetermined constants is omitted. The displacement boundary conditions are satisfied strictly on clamped edges, and it is not necessary to divide the layer with same material into some sub-layers. Therefore the obtained solutions are more accurate. Additionally, a new calculating method of the stresses on the clamped edges is proposed and more exact boundary stresses can be obtained. The results of two examples show that the present solutions have better constringency and higher precision, and are approaching to FEM solutions well than the existing exact solutions, especially on the clamped edges.