This paper presents an analytical approach to the problem of scalar wave scattering from a slightly rough random surface with the Dirichlet or the Neumann boundary condition. The Green's function method is employed to analyze statistical characteristics of waves including multiple scattering. The integral equations for the first and second moments of scattered waves are derived in a unified form for both boundary conditions. Iterative solutions for the intensity of coherent and incoherent waves are then obtained and are shown to satisfy energy conservation. The effects of multiple scattering due to surface roughness are incorporated systematically into those solutions through an effective surface impedance. Numerical results of the first-order solutions for the incoherent wave show that even for slightly rough surfaces multiple scattering effects are pronounced in the Neumann case at near-grazing incidence when the correlation length of the surface height is smaller than the wavelength. In the Dirichlet case, such effects appear at angles near normal incidence, but are not so significant. The results obtained herein are also compared with those previously obtained under the same perturbation boundary condition.