The third‐order elastic constants of 26 cubic crystals and two mixed crystals belonging to octahedral class have been evaluated from the available literature data on the hydrostatic pressure variation of the corresponding second‐order constants using the method elaborated [O. H. Prasad and M. Suryanarayana Acustica38, 192–193 (1977)] wherein the third‐order constants can be evaluated without any reference to uniaxial stress measurements. The evaluated third‐order constants for each of the crystals are used in the well‐known equations [W. P. Mason and T. B. Bateman, J. Acoust. Soc. Am.36, 644–652 (1964)] to obtain the 39 mode gammas all of which add up to give the Gruneisen parameter γ of the crystal in question. The correctness of the evaluated parameters is verified by evaluating the thermal expansivity α of each crystal using the familiar equation connecting α with γ The crystals studied are NaCl, NaBr, NaF, LiF, KCl, KBr, KI, KF, RbCl, RbBr, RbI, AgCl, AgBr, MgO, CsBr, Nb, Fe‐α, Ag, Cu, Au, Al, Ge, Si, ZnSe, ZnTe, RbAg4I5, and mixed crystals AgCl‐AgBr and KCl‐KBr near room temperature and in a few cases at different temperatures and pressures.