Using the local-density approximation, and calculating the Hellmann-Feynman forces, the stability of the perovskite-like structures of CaTiO3 have been studied by applying the direct method and deriving the phonon dispersion relations. The cubic Pm (3) over barm phase shows dispersionless soft phonon branch spreading from R to M points of the cubic Brillouin zone. Low-symmetry phase I4/mcm can be considered as a result of the soft mode condensation at R point. The experimentally observed Pmnb phase is a consequence of the intersection of Imma and P4/mbm space groups, being the result of soft mode condensation at R and M points, respectively. Thus, the Pmnb can be regarded as simultaneous condensations of two soft modes. The phonon dispersion relations of Pmnb suggest that this phase is stable. (C) 2001 American Institute of Physics.