The moment method solution of the problem of input impedance and mutual coupling of rectangular microstrip patch antennas fed by microstrip transmission line is presented. The formulation uses the grounded dielectric slab Green's function to account for the presence of the substrate and surface waves. In our problem replaced the patch by equivalent source, which is represented by mode summation, the reaction between the impressed and induced surface current is defined. And the reaction integral is calculated by Gaussian quadrature. The calculated mutual impedance is compared with other calculation at 2282MHz and measured data in $22.7mm\times28.4mm$ copper clad woven polytetrafluoroethylene/glass laminate plat at 4052MHz for both E-plane and H-plane coupling. The result has shown that the agreement in tendency between measured and calculated data is good and the errors in other point except the 0.55$\lambda_o$ and 1.1$\lambda_o$ are less than 11%