Abstract: Free vibration problems in plane compressed orthotropic rectangular thin plates on two parameter elastic foundation can be solved in two cases. When a plate is simply supported at four edges, it can be solved by double sine sery method to get each proper frequency. In other arbitrary boundary conditions, it can be solved by the method of separating the variables to get each algebraic polynomial solutions and single sine series solutions firstly, and then establishing a general solution that can be used to satisfying arbitrary boundary conditions of four edges and four corners except simply supported at four edges. The integral constants in general solution can be determined by boundary conditions. For example, a square plate with four edges simply supported and clamped have been calculated and analyzed. This method is simple and complete, and easy to use in practice. All formulas in this paper can be applied to solve stability problems. By assuming that the proper frequency of the plate equals to zero, the ratio of compressed forces of two opposite edges or one of them is known, each critical compressions can be obtained.