We consider the materials formed by the homogeneous matrix and periodically arranged multi-layered inclusions with the dispersed or fibrous particles of spherical, spheroidal or cylindrical form. It applied the method of radial multipliers to simulate the physical processes in these materials, which allows to construct in compact form via Papkovich-Neuber representation, the system of basis functions for a wide range of problems, including the theory of elasticity, thermal conductivity and filtration. These systems analytically exactly satisfy the original equation and contact conditions on the interphase boundaries. These functions are used for solving the problems of mechanics of heterogeneous media with multi-layered inclusions of spherical, spheroidal and cylindrical form by the block method of least squares. In particular, they are used for estimation with a high degree of accuracy by asymptotic homogenization method of effective characteristics and internal micro-fields in heterogeneous materials, as well as for direct modeling of physical processes in structurally inhomogeneous materials.