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We report here some theoretical results on the parametric excitation of spin waves by an elastic wave, together with experimental observations consistent with these results.A phonon traveling in a magnetically saturated ferromagnet generates an effective magnetic field that can parametrically couple to spin waves. This field has the phonon momentum and, hence, spin-wave excitation by a traveling-wave pump is possible. The effective field may, in general, have components that are both transverse and parallel to the dc magnetic field. The former lead to modified Suhl instabilities, 1 the latter to modified "parallel pump" instabilities. 2 ' 3 We restrict ourselves here to a discussion of the instabilities excited by a longitudinal phonon of frequency uu,, and elastic displacementwhose wave vector, kp = i z kp, is parallel to the dc magnetic field. We consider the first-order excitation of spin-wave pairs when the pump phonon travels in a cubic crystal of ellipsoidal shape magnetically saturated along a principal axis taken, for simplicity, parallel to a (100) crystal axis. The classical equations of motion governing spin-wave propagation follow from aM/8* = y MxH,in which y denotes the gyromagnetic ratio (negative). The magnetization is assumed to be composed of a spin-wave pair, m x and m 2 , so that M = mi+ m2+i z M s . The ith spin wave, whose wave vector isy ty it ty and M s denotes the saturation magnetization. To account for the Zeeman, demagnetizing, exchange, dipolar, and magnetic anisotropy energies and to include loss, H = h} +h2+%H z , where h. = -\k 2 m .-47T ri it k: k.(k.-m.) AH. r 2M x ty y tx K t s and H =H-4*N M +2K/M . z 0 z s Is (6)