We have used first principles total energy pseudopotential techniques to calculate the ground state properties and the relative stabilities of the high pressure phases of the beryllium chalcogenides BeSe, BeTe, and BeS. We study the energy-volume (E-V) relations of the zincblende, NaCl, CsCl, NiAs, and P S n structures of these compounds. The components of the stress tensor were also calculated and used in the structural relaxation of the tetragonal and hexagonal phases. From the E-V curves of the structures considered and the Gibbs construction we find that these compounds transform under pressure from the zincblende structure (B3) to the NiAs structure (B8), and no further transitions are found. Our calculated values of the structural parameters and the B3 + B8 transition pressure for BeSe and BeTe agree well with recent experimental results. Very little is known experimentally for BeS, and our results for this compound have a predictive character.