The effect of a magnetic field on the magnetically controllable cooperative Jahn-Teller distortion in DyVO4 has been investigated. Results are presented of calculations of the temperature and field dependence of the strain distortion e11-e22 and the elastic constant c11-c12, the temperature (strain) dependence of the g factors and the paramagnetic susceptibility tensor, and the temperature and field dependence of the four-low-lying crystal-field levels. For fields in the x y plane, a phase transition occurs only for |Hx|=|Hy|. For all other orientations in the plane, the field induces a distortion which persists to all temperatures. For fields along the z axis a first-order transition to a new magnetic phase is predicted, the stability limit of which has been calculated as function of temperature and field. The excitation frequency determined by the separation of the middle-two crystal-field levels goes to zero at the stability limit and is the soft-mode frequency associated with the transition. © 1974 The American Physical Society.