This paper shows why a static pressure of several megabars can be reached in a diamond anvil cell using a molybdenum gasket whose yield strength at P=0 is only 0.04 Mbars. The elastic constants of bcc Mo at 0 K vs reduced volume and pressure were otained from first-principle, all-electron, density-functional calculations to V/${\mathit{V}}_{0}$=0.4 (P=11.6 Mbars) although the fcc phase was calculated to be more stable above 6 Mbars. These constants were used to obtain the Chua and Ruoff pressure scaling factor for the yield strength which combined with plasticity theory shows that a gasket of 2.6 \ensuremath{\mu}m final thickness can support 6 Mbars.