<p>We construct a mathematical model of the diffusion of admixtures in a two-phase body with spherical inclusions located near the boundaries of the body under the conditions of imperfect contact for the concentration function on the interfaces. By using the equation of normal to the surface for a spherical inclusion, we obtain the diffusion equation for the entire body, formulate the required contact conditions, and deduce the Volterra–Hammerstein integrodifferential equation with random kernel. The solution of this equation is obtained by the method of successive iterations in the form of a Neumann series. The random field of concentrations is averaged for special cases of the beta-distribution of inclusions used to describe the structure with the most probable location of the inclusions near the boundaries of the body. The formulas for the evaluation of the concentrations of admixture particles in two-phase bodies with spherical inclusions are obtained.</p>