On the basis of Navier’s solution to rectangular plates, the bending problem was studied for the four edges supported thin plates under local uniformly distributed load, where the double Fourier series with additional terms was adopted as the deflection function of the plates. Linear algebraic equations for solving the undetermined coefficients were derived. A unified solution was obtained to the rectangular plates with clamped and simply supported edges. The rate of convergence was discussed on the solution of the series method with additional terms. The proposed method was compared both with superposition series method on accuracy, and with finite element numerical method on computational cost. The results show that 40 terms should be employed for a convergence of the series. The method with additional terms shows the same accuracy of solution as superposition series method does. The solution by finite element method gradually approaches that by the series method as the mesh gets finer and finer. In comparison with finite element method, the computational time by the series method is negligible. This work is applicable for structural analysis of the top plates of underground buildings under truck wheel pressure.