We perform a linearization of the transcendental equations for the moments of the single-particle atomic distribution functions of an anharmonic crystal with a surface. The transcendental equations can be derived from the nonlinear integral equations of the nonsymmetrized self-consistent field method. With the help of these equations we consider the relaxation of the lattice of an fcc crystal near its three surfaces and the mean square displacement of the atoms, assuming nearest-neighbor interactions. We discuss effects which result when interactions between nonnearest-neighbors are taken into account and also the application of the method to small cyrstalline particles. © 1986 Plenum Publishing Corporation.