The relative stability of various high-pressure phases of CsI is studied from first principles and analyzed using the Landau theory of phase transitions. We demonstrate that the cubic-to-orthorhombic transition recently observed to occur slightly below 20 Gpa is driven by the softening of an acoustic phonon at the M point of the Brillouin zone. The coupling between this mode and anisotropic strain makes the transition slightly first order (with a volume variation of the order of 0. 1%), and stabilizes the experimentally observed orthorhombic phase with respect to other competing symmetry-allowed structures. [1,3] nor theoretical [4][5][6][7] work. In particular, though the cubic-to-tetragonal transition has been theoretically predicted by both semiempirical [4] and first-principles [5,6] calculations, no evidence of the further orthorhombic distortion has been found by either methods [7].Recent experiments [8,9] suggest that CsI undergoes a continuous transition from the cubic (82) to an hcp structure, passing through an orthorhombic phase, C2," which is, however, different from the previously proposed structure [2], Dzi, . In this paper we study the relative stability of various phases of CsI at high pressure (cubic, tetragonal, and the newly proposed orthorhombic structure). We identify the amplitude of a sixfold-degenerate phonon mode (M5 ) as the relevant order parameter of the transition in the Landau sense. The frequency of this phonon is found to vanish at a pressure of = 23 GPa, which is well below the transition from the cubic to the tetragonal phase. Neglecting the coupling between the soft mode and anisotropic macroscopic strain, we find that the transition would be second order from the cubic to a tetrahedral (T ) phase; the coupling with macroscopic strain stabilizes the orthorhombic structure, making the transition first order, with a very small volume change (=0.1%) and a transition pressure (= 21 GPa) slightly below the softening pressure of the M5 phonon.We also find that the orthorhombic structure is always favored with respect to the tetragonal structure, up to pressures of 60 GPa.The cubic-to-tetragonal transition reported in Refs.[ (110) direction.In fact, the gliding of one of the (110) planes -which was indicated in Ref. [8]