The tremendous elastic stresses appearing during the growth of single crystal substrates with the lattice parameter strongly differing from the lattice parameter of the substrate do not allow us to obtain high quality layers of new broad band semiconductors without misfit dislocations. It is assumed that the currently most promising of these are silicon carbide SiC, gal lium nitride GaN, aluminum nitride AlN, boron nitride BN, and zinc oxide ZnO [1]. Integration of these materials into the silicon electronics plays a key role for the development of industrial technologies; therefore, it is very important to grow epitaxial films of these materials just on silicon [1]. However, due to the large difference in lattice parameters of silicon and all the mentioned broad band semiconductors, i.e., dur ing the ordered growth of these materials (~20%), elastic energy rises on the surface of silicon single crys tals. This leads to the appearance of a tremendous number of misfit dislocations of the lattices growing outside and even to complete film cracking. Charge carriers are scattered by dislocations; this makes it impossible to use such samples in semiconductor devices.We suggest using a new in principle relaxation mechanism of the elastic energy for growing disloca tion free heteroepitaxial films. The essence of this approach, which differs from all the existing methods of film growth, is based on the idea of preliminary incorporation of point defects, of which the skeleton of the future film will be collected, into the crystal lat tice of the silicon host. When growing the SiC film on the Si substrate, such defects are the carbon atom C incorporated in the Si interstice and the vacancy formed as a result of removal of one of the Si atoms. If these defects are attracted to one another by the elastic mechanical interaction in the silicon matrix, the sum mary elastic energy caused by their incorporation into the substrate host is considerably lower than the energy of noninteracting defects. It is well known that the spherically symmetric dilatation centers do not interact with each other at all in an isotropic medium of infinite sizes [2]. In this work, we show that the dila tation centers can attract each other in substantially anisotropic media, such as the crystal with the cubic lattice symmetry, thereby considerably decreasing the total elastic energy [2]. Such attractive centers form stable objects of a new type, the elastic dilatation dipoles. We computed the elastic energy of the system by the example of heteroepitaxy of the SiC film on the Si substrate (Si has a cubic lattice) and showed that the MECHANICS Abstract-It is shown that in substantially anisotropic media, such as a crystal with cubic lattice symmetry, the analogous dilatation centers can strongly attract each other considerably decreasing the total elastic energy. Such attractive centers form stable objects of a new type, the elastic dilatation dipoles. By the example of heteroepitaxy of the film of silicon carbide SiC on a silicon substrate, the calcu...