The free vibration characteristics of rectangular thin plates with four-point supports at different locations are studied. Firstly, the lateral constraint springs are introduced at different locations of the plate structure model, and the stiffness values of artificial springs are set to simulate the boundary conditions of four-point supports. Then based on the two-dimensional modified Fourier series, the admissible displacement function of the structure is expressed, in which the additional terms of the improved parts can solve the discontinuity problem of the derivatives of the displacement function on the boundary. The energy functional of the rectangular plate system is established, and the linear equations are established by letting the functional choose the stationery value. Finally, the free vibration frequency parameters of the point-supported rectangular plate are obtained by solving matrix eigenvalue problems, and the vibration characteristics of the rectangular plate supported by four points at different positions are given. In the two-dimensional modified Fourier series method, the additional terms can improve the accuracy and rate of convergence. The research results provide some reference for the free vibration of rectangular plates supported at different points.