The isotope shifts in the isotropic hyperfine coupling constants of certain isotopically substituted methyl radicals are evaluated from vibronic wave functions in the Born-Oppenheimer approximation, with the electronic wave function calculated via self-consistent field molecular orbital theory with the INDO approximations for atomic and molecular integrals. The theory at this level of approximation is found to accommodate quite well the trends in the experimentally observed quantities, and to provide a basis for a discussion of the reasons for the observed trends in terms of the orbital description of electronic structure.