Abstract In this article, the highly compressed matter has been considered as a model for simple anisotropic metals. A perturbation method was set up to determine the energy spectrum of a Fermi system in a periodic field. By taking account of the static potential of ion lattice, the Coulomb interaction and interaction via phonon fields, the spectrum of single particle excitations was studied. Detailed calculations of the Fermi surfaces and the density of states have been carried out for f.c.c. and b.c.c. lattices, with the numerical results presented in Fig.8-Fig.10.