The three-dimensional problem of admixture diffusion is considered in a semispace of random geometrical configuration composed of N + 1 phases under action of a constant source on the body surface. The used approach for description of admixture transfer in a random nonhomogeneous body allows for both jump discontinuities of a diffusion coefficient on interphases and equally probable distribution of spherical inclusions in the body. Admixture concentration averaged over the ensemble of phase configurations has been obtained under consideration of medium nonhomogeneities as internal sources. (C) 2003 Elsevier Science Ltd. All rights reserved.