The well‐known Morse function &phgr;(r) =D{exp [−2&agr;(r−r0)] −2 exp [−&agr;(r−r0)]} can be considered to be a particular case of the general family of potential functions with exponential attraction and exponential repulsion, viz., &phgr;m(r) = [D/(m−1)] {exp[−m&agr;(r−r0)] −m× exp[−&agr;(r−r0)]}. This study examines the suitability of applying the functions &phgr;m(r) to the description of mechanical properties of cubic crystals. For bcc lattices, the ratioC11/C12for the theoretical model of the crystal made up of atoms with &phgr;m(r) interatomic interactions is shown to be too small to provide a realistic description of bcc metals; also, the bcc crystals are found to be inherently unstable for larger values of &agr;a0, wherea0is the lattice parameter of the crystal. For fcc lattices, however, the theoretical model of the crystal is found to be mechanically stable for arbitrary (i.e.,m>1) exponentially attractive and repulsive interactions and the elastic moduliC11andC12of the theoretical fcc crystals are found to be capable of conforming to the respective experimental values of fcc metals. The results are in agreement with Born's analyses of lattice stability. Numerical values ofD, &agr;, andr0are calculated for several different values of the parametermfor fcc Ni using experimental values ofC11,C12, and lattice parameter. The element Ni is selected because, among the fcc metals, Ni most closely obeys the Cauchy conditionC12=C44. The functions &phgr;mare then used to calculate theoretical pressure versus volume (P‐V) behavior (at pressures large enough to produce considerable anharmonicity) and the results are compared with experiment; good agreement is found between the calculated and experimentalP‐Vrelations.