[en] This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of ($n\ge <!--\; ???\; -->2$) for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0–600 GPa. (methodological notes)