Within the framework of the pair potential approximation and the shell mode
l including the Jahn-Teller contribution to the crystal energy we have stud
ied the elastic properties of La2CuO4. The strong anisotropic correlation b
etween the lattice deformations e(xx) and e(zz) and the internal displaceme
nts of the accompanying sublattices within the La2O2 layers 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 orthorho
mbic phase region neat the pressure-induced structural phase transition. Bu
t we have not observed the softening of c(11), c(12), and c(66) in the tetr
agonal phase region that was measured near the temperature-induced structur
al phase transition.