Crystalline lattice can become unstable to the uniform shear strains which may lead to a structural transformation to less symmetric structures. The transitions of these types were called the elastic phase transitions. In the present paper the elastic phase transitions in metals with cubic and hexagonal structures are considered. The relation between the elastic constants of second, third and fourth order corresponding to the case of the first order elastic phase transition are given. As an example the structural transformation in vanadium which is experimentally observed at P ≈ 69 GPa, and a possibility of the structural transformation in molybdenum at P higher than 700 GPa are analyzed.