We study the influence of anisotropy, treated as a dimensional crossover between 1D and 3D systems, on the topological instability induced by a (self-consistent) uniaxial periodic potential. The mechanism on which the instability is based involves the topological reconstruction of the Fermi surface, from initially closed pockets to the surface with open Fermi sheets, creating two peculiar points in the band dispersion—the saddle point and elliptical point, between which the pseudogap in electron density of states develops. The self-consistent periodic potential appears as a result of interactions, either electron-phonon or electron-electron, which, linked with the topological instability of the system, results in formation of a new ground state of the system—the density wave provided that the relevant coupling constant is larger than critical. Our analysis shows that the phase transition takes place along the whole continuous interval of a dimensional crossover between 1D and 3D, but that the critical coupling strength significantly increases with the dimensionality of the system. It is our intention to give an initial framework for understanding the nature of charge density waves experimentally observed in a number of materials, like high-Tc cuprates or graphite intercalates, both being materials with a closed, rather isotropic Fermi surface far from the nesting regime