Diffusion research is important for understanding of many processes based on mass transfer. In many respects, diffusion, determines physical and mechanical characteristics for new materials with fine-dispersed matter and a large number of grain boundaries and phases. Models of diffusion along grain boundaries and their modifications are widely known in literature, but they are not always applicable to nanomaterials due to indistinct determination of some notions. At the present paper the model of diffusion is presented, which considers boundaries and area near boundaries as a phase with special properties. Mass transfer between the volume of a grain and a boundary phase is taken into account. The approximate analytical solution of the problem is formulated. In the general case the problem is solved numerically. Non monotonic distributions of concentrations in volume are obtained.