A detailed theory is developed for first‐order transverse pumping mechanisms arising from terms in the magnetocrystalline energy which are linear in strain. A physical description of these mechanisms is given in terms of direct and indirect interactions among the particle displacement and magnetization variables, and the instabilities of the medium are classified as direct or indirect according to the mechanisms involved. Numerical values of the thresholds are calculated as a function of propagation angle for longitudinal magnetoelastic instabilities in YIG pumped at 1000 Mc/sec. It is shown that two magnetoelastic instabilities have thresholds which are substantially lower than the second‐order spin‐wave instability threshold. The implications of this result relative to the parametric amplification of elastic waves and the interpretation of certain anomalous saturation effects in ferrites are discussed.