A calculation is presented which describes the splitting of doubly degenerate electronic states of tetragonal and trigonal centres in cubic crystals by an applied uniaxial stress. It is shown that the shift and splitting of the states may be expressed in both cases in terms of four independent parameters. The approach follows that originally used by Kaplyanskii in 1964 for anisotropic centres having non-degenerate states and cubic centres having degenerate states. The calculation is used to tabulate the energy shifts of lines in the uniaxial stress spectra of A → E and E → E transitions within centres of tetragonal and trigonal symmetry, and the results are illustrated by application to the 3932 A and 4874 A colour centre zero-phonon absorption lines in lithium fluoride.