It is found that one of the six third-order constants of cubic crystals of sufficiently high symmetry and two combinations of the remaining five constants relate to strains in which the volume is unchanged. These shear constants are 1/8(C₁₁₁-3C₁₁₂+2C₁₂₃), C₄₅₆ and ½(C₁₄₄-C₁₅₅). The electrostatic and repulsive ion-ion contributions to these constants are obtained in general terms for face-centred cubic and body-centred cubic metals. The electrostatic contributions are positive for face-centred cubic metals and negative for body-centred cubic metals. The repulsive contribution to C₄₅₆ is relatively insignificant in face-centred cubic metals whereas it predominates in body-centred cubic metals.These two contributions are not able to account for the observed third-order shear constants of noble metals, particularly C₄₅₆. It is shown that it is necessary to include the energy of the conduction electrons. Detailed calculations cannot be made, however, until the third-order constants have been determined at low temperatures.