The rare-earth crystals DyVO
4
, DyAsO
4
and TbVO
4
undergo structural phase transitions at 14, 12 and 34 K respectively induced by a cooperative Jahn-Teller effect. An experimental investigation of the phase changes has been made using Raman scattering methods. For purposes of comparison, the Raman spectra of DyPO
4
, YVO
4
and GdVO
4
(which do not undergo phase transitions) have also been measured. A detailed theory of the phase transitions has been developed which accounts for the electronic and vibrational Raman spectra. The lowest four electronic levels of Dy
3+
and Tb
3+
are treated in a pseudospin formalism, and the theory is discussed in terms of mixed phonon and pseudo-spin excitations. The singly degenerate
κ
≈ 0 optic phonons are not measurably affected by the transitions, but splittings of up to 20 cm
-1
developed in the doubly degenerate E
g
phonon modes in the Raman spectra owing to anharmonic couplings with the electronic states. Splittings are also observed in the lowest electronic levels of the rate earth ions below the transition temperature; these electronic modes effectively constitute the soft mode which causes the transitions to occur. A molecular field model is first used in the theoretical analysis. The equations of motion of the coupled excitations are then found and the energies, line widths and dispersion of the mixed excitations are discussed. The connexion between the static strain and the acoustic phonon mode coupling is investigated, and a thermodynamic treatment of the elastic constants is given. From the Raman data, it appears that in TbVO
4
the acoustic mode coupling is stronger than the optic mode coupling.
