The Mueller matrix describes the influence of an object on the polarization of optical waves. It has various information about the object surface. In this paper, the scattering field and the scattering Mueller matrix of two-dimensional random rough surfaces are analyzed using the Kirchhoff approximation method. The scattering Mueller matrices of copper, iron, nickel, glass, and lithium niobate are numerically simulated using the incidence angle, and the relative roughness is changed. With the increase of the incident angle, the m01, m10, m22, and m33 parameters of metals and dielectrics vary by less than 30% and greater than 80%, respectively. The m00, m11, m22, and m33 parameters of metals and dielectrics vary by more than 60% and less than 20%, respectively. Further, the m23 and m32 parameters of metals are increased as the incident angle increases, and are decreased as the relative roughness increases, whereas the m23 and m32 parameters of the dielectric are always 0. The differences can be used for identifying metal and dielectric and provide some reference to the measurement of object surface roughness.