An analysis of crystal structure stability against homogeneous deformation is carried out for simple and transition metals with body-centered cubic (bcc) and face-centered cubic (fcc) lattices under pressure. It is shown that at high compression ratios a crystal lattice can turn unstable against shear deformations, leading to new lower-symmetry structures. To analyze these structures, the Landau theory of phase transitions with finite deformation tensor components as order parameters is applied. A comparison is made with experimental data on high-pressure phases. Prospects are discussed for using the suggested approach to explain structural transformations in solids at high pressures.