Within the framework of the pair potential approximation and the shell model including the Jahn-Teller contribution to the crystal energy we have studied the elastic properties of La2 CuO4 . The strong anisotropic correlation between the lattice deformations exx and ezz and the internal displacements of the accompanying sublattices within the La2 O2layers are shown to be responsible for the giant anisotropy of the elastic moduli in the xz -plane. We have predicted the softening of several elastic moduli in the orthorhombic phase region near the pressure-induced structural phase transition. But we have not observed the softening of c11 , c12 , and c66in the tetragonal phase region that was measured near the temperature-induced structural phase transition.