Cr2+ centres in SrF2 and CaF2 are strongly coupled Jahn-Teller systems. A theoretical Jahn-Teller model is developed, in which the parameters that appear in the effective Hamiltonian describing the 5T2g ground state of the Cr2+ ion are obtained by fitting previously published EPR results. It is found necessary to include certain random strains in the analysis in order to explain the orthorhombic features of the EPR spectra. The coupling between the ground and excited states and the effects of other perturbations are discussed.