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A general method for the calculation of parallel pump instability thresholds of magnetoelastic waves is presented. The analysis takes into account variation in direction of applied field and propagation vector in the crystal lattice, and the effects of magnetoelastic anisotropy are included. It is found that variation in the direction of propagation is expected to modify the shape of experimentally observed phonon pips, and experimental results are presented in accordance with this view. The values obtained for elastic factors using this interpretation of the data are considerably lower than those obtained under the usual assumption of propagation in the plane normal to the steady field. An estimate is made of the influence of small elastic anisotropy on the observed line shape.