  The elastic anomaly observed in the coherent Kondo state of Ce heavy fermion
compounds is analyzed by using the Anderson lattice model simulating the energy
level scheme of CeTe. The $\Gamma_7$ doublets and $\Gamma_8$ quartets of the 4f
states are considered in the model. We solve the mean field equations to derive
the temperature dependences of elastic constants, using the random phase
approximation like expression for the interaction between the elastic strain
and the crystalline field splitting. We compare the calculation with the
$(c_{11} - c_{12})/2$ and $c_{44}$ constants of CeTe. The presence of the
downward dip and the observed overall temperature variations of the two
constants are well described by the present theory. The origin of the dip is
the coupling between the elastic strain and the splitting of the $\Gamma_8$
quartets.
