This article deduced a theoretical method to obtain the second order partial der ivatice of shear modulus with respect to pressure G″P from the theor y of electron structure for crystal materials.We obtained G″P0=-0.033GPa-1 for 93 tungsten alloy,and applied this result in the fini te strain theory of Birch-Murnaghan,when comparing the calculated results of G″ P0=-0.033GPa-1 with the results of G″P=0, we find the results of G″P=0 are greater than that of the results o f G″P≠0.The difference between them becomes greater when the pressu re increases. Therefore,we can conclude that G″P cannot be neglected at high pressures.