Abstract The generalized Lindemann's criterion is utilized to derive the variation of the melting temperature T m with compression. The result incorporates the basic features of the lattice potential as well as the volume dependence of the frequency distribution through the first two moments of the mode Grüneisen parameter. This melting relation predicts that when T m is plotted against the volume of the melting solid, the fusion curves of solids bonded by Van der Waals forces are concave to the temperature axis and in accordance with the predictions of the Simon equation. On the other hand, the predicted melting curves of ionic compounds, as the alkali-halides, are concave to the volume axis and exhibit a maxima at higher pressures. Since silicates generally possess an ionic contribution to the lattice energy, this melting relation should give a more accurate estimate of the high pressure melting temperature for these compounds than Simon's and theoretically similar equations.