Demonstrating for the first time the applicability and accuracy of the finite strain difference method with ab initio molecular dynamics to MOF systems, we provide the first reliable value for the bulk modulus of an amorphous ZIF in the literature. We find that ZIF-4 glasses have a larger bulk modulus than the crystal, and confirm previous results which found the density to be larger for the glass phase. Not only does this study provide intrinsically valuable data, it yields reference values for the computation of finite temperature mechanical properties, making it possible to validate alternative methods with less computationally expensive MD schemes.