In the frame of density functional theory, first principles calculations were carried out to determine pressure stability ranges of zinc-blende (B3), cinnabar (Cinn), rock-salt (B1), orthorhombic (Cmcm), and cesium chloride (B2) phases of CdTe. In agreement with experimental observations, we found a B3 → Cinn → B1 → Cmcm pressure-induced sequence, and predict the B2 phase as a potential high pressure polymorph. The equations of state of all these polymorphs and the components of the elasticity tensor of the B3 phase at zero pressure were determined and microscopically analyzed in terms of atomic contributions. The concept of local pressure allows for quantifying differences in the role played by Cd and Te as regards the compressibility of CdTe phases, and suggests the existence of a general behavior under pressure for binary II-VI semiconductors.