The effect of hydrostatic pressure on the stability of precipitates in the Al–Li and Cu–Be alloy systems has been examined using a first-principles method. The solid-phase portion of the Cu–Be and Al–Li phase diagrams has been computed from first-principles. In the case of Cu–Be no adequate description of the thermodynamics could be obtained, and consequently no realistic phase diagram could not be computed. However, an analysis of a Calphad type calculation indicates why the current method fails. For Al–Li a good cluster expansion could be obtained and the computed zero pressure phase diagram exhibited excellent agreement with the experimental data. A high pressure phase diagram was computed as well. It is predicted that phase equilibria in the Al–Li system are little affected by compression. Compression does not affect the Al–Al₃Li metastable phase equilibria but the calculated equilibrium isothermal solubility of Li in Al is decreased, in agreement with recent measurements.