The mean irradiance reflected from a randomly rough dielectric surface is calculated using the vector Kirchoff integral. The tangent‐plane approximation is used to relate the fields on the boundary to the incident fields through the Fresnel reflection coefficients. The averages involving the random surface variables are performed exactly using a spectral representation for the scattering function. The special case of a corrugated surface is treated numerically to gain insight into the more general problem. Our results are compared with previous solutions. An empirical formula is presented for practical applications. Finally, a general expression for the depolarization matrix is derived, retaining terms up to second order in the surface slopes. Our solution is compared with available theories.