Modification of the nuclear matrix elements for transitions between the ground state of a nucleus and accessible excited states of the nucleus formed by neutrino capture on the original nucleus are calculated on the basis of a deformed shell model where the initial and/or final nuclei involved may be deformed. It is shown that as long as there are different deformations in the initial and final nuclear states, the beta transition rates may be reduced by factors of two to three from the values they would have if there were no deformations. These considerations are applied to calculate neutrino capture rates in and in .