We study the behavior of alpha cristobalite under anisotropic stresses using constant-pressure ab initio simulations and observe the formation of the anataselike, stishovite, and CaCl(2)-type structures depending on the degree of hydrostatic compression. These phase transformations proceed via a tetragonal intermediate phase (phase X-I) within P4(1)2(1)2 symmetry or an orthorhombic intermediate state, having space group of P2(1)2(1)2(1). The phase transitions into stishovite and the anataselike phase are based on the same intermediate state. The compression of alpha cristobalite along the c direction produces stishovite while the expansion of alpha cristobalite along the c direction yields an anataselike phase. The energy-volume calculations suggest that alpha cristobalite can transform into the anataselike structure if and only if the phase transition into stishovite is suppressed. A phase transition between stishovite and anatase, however, is unlikely to occur.