<p>Effects of the magnetic field and compressive stress on the reflection and transmission of elastic waves obliquely incident at the interface between two piezomagnetic half-spaces are investigated in this article. The constitutive relations of piezomagnetic materials are derived from the Zheng − Liu model. The effective elastic, piezomagnetic, and magnetic permeability constants are functions of the applied magnetic field and compressive stress. By satisfying the interface continuity conditions, the reflection/transmission coefficients (RTCs) of elastic waves are obtained. Results show that the reflection angles of bulk waves are nearly unaffected by the magnetic field and compressive stress when quasi-pressure (QP) waves are incident from Ni6 to Terfenol − D. The reflection angles of the bulk wave that has the same mode as the incident wave are not affected by the magnetic field and compressive stress when QP waves are incident from Terfenol − D to Ni6. The RTCs exhibit complex and non-monotonic variation patterns with the incident angle under the magnetic field and compressive stress. By appropriately adjusting the incident angle, magnetic field, and compressive stress, the transmitted bulk waves disappear or the reflected and transmitted waves have the same mode as the incident wave. The findings presented in this article establish a theoretical basis for the design of actively controllable vibration isolators and noise attenuation devices.</p>