A new magnetoelastic resonance effect is described. A dc magnetic field was applied in the long direction of YIG slabs (1 cm long, 0.5 cm wide, and 0.1 or 0.07 cm high), each end of which was inserted in a stripline cavity. Under appropriate conditions a pulse of microwave power applied to one cavity resulted in a pulse in the second cavity delayed by several microseconds. Small variations were observed in the amplitude of the delayed pulse as the dc field was varied. Similar variations with the same periodicity (∼1 Oe) were also observed in the undelayed reflection from the input cavity. The amplitude variation is attributed to the excitation of magnetoelastic resonances in the nonuniform magnetic field near the endface of the sample. Because of the strong coupling between spin waves and elastic waves, the turning point (at whichkspin waves=0) and the endface of the sample define a magnetoelastic quasicavity whose resonances give rise to the effect noted. According to this interpretation the separation of adjacent peaks should be &dgr;H= |H′dem|&lgr;/2, whereH′demis the gradient of the demagnetizing field evaluated at the crossover point (kspin wave=kphonon) and &lgr; the wavelength of transverse elastic waves. Measurements have been made showing the dependence on dc field, slab thickness, and frequency. Agreement with theory is satisfactory.