The paper describes the homogenization procedure for two-phase mixture elastic composites that consist of two isotropic phases. It is assumed that on the boundary between the phases, special interface boundary conditions are held, where the stress jumps over the interphase boundary are equal to the surface stresses at the interface. Such boundary conditions are used for description of nanoscale effects in elastic nanobodies and nanocomposites. The homogenization problems are solved using the approach of the effective moduli method, the finite element method and the algorithm for generating the representative volume that consists of cubic finite elements with random distribution of element material properties. To provide a numerical example, a wolfram-copper composite is considered, where the interface conditions are modeled by surface membrane elements.