We analyzed a periodic thick mushroom structure for use as an artificial magnetic conductor using mode-matching method. The fields in each region were represented by either Floquet modes or waveguide modes. By applying tangential electric and magnetic field continuity conditions and using matrix equations, unknown coefficients and dispersion diagram were calculated. The proposed model can account for the effects of oblique incidence. Simulation time using the method was much faster than the commercial tools. We found that the current method produces accurate results of reflection phase and dispersion diagram.