The instability threshold of magnetoelastic waves has been calculated for arbitrary angle &thgr; between the dc magnetic field and the direction of propagation for the case in which the frequency of the potentially unstable vibrations is either considerably smaller or considerably larger than the crossover frequency of the magnon‐phonon dispersion diagram. Under these conditions, the vibrations are substantially pure phonons. When magnetic losses are neglected, the lowest critical field is of the order ofhcrit≃&ohgr;/&ggr;&sgr;&tgr;e, where &sgr;=&ggr;b22/C44M0, &ohgr; is the pump frequency, &ggr; the gyromagnetic ratio, &tgr;ethe elastic relaxation time,b2the magnetoelastic constant,C44the shear modulus, andM0the saturation magnetization. If half the pump frequency is less than the crossover frequency, the lowest threshold occurs for transverse waves that propagate at an intermediate (and typically rather small) angle to the dc field direction; if it is larger than the crossover frequency, the lowest threshold occurs for transverse waves having &thgr;=&pgr;/2. The influence of magnetic loss upon the threshold is small for low‐loss materials such as yttrium‐iron garnet as long as the frequency of the unstable vibrations is not too close to the crossover frequency.