An analytical and numerical approach is developed to pinpoint the optimal experimental conditions to irreversibly switch magnetization using surface acoustic waves (SAWs). The layers are magnetized perpendicular to the plane and two switching mechanisms are considered. In processional switching, a small in-plane field initially tilts the magnetization and the passage of the SAW modifies the magnetic anisotropy parameters through inverse magnetostriction. The SAW triggers precession and, eventually, reversal. Using the micromagnetic parameters of a fully characterized layer of the magnetic semiconductor (Ga,Mn)(As,P), we show that there is a large window of accessible experimental conditions (SAW amplitude/wave-vector, field amplitude/orientation) allowing irreversible switching. As this is a resonant process, the influence of the detuning of the SAW frequency to the magnetic system's eigenfrequency is also explored. Finally, another-nonresonant-switching mechanism is briefly contemplated and found to be applicable to (Ga,Mn)(As,P): SAW-assisted domain nucleation. In this case, a small perpendicular field is applied opposite the initial magnetization and the passage of the SAW lowers the domain nucleation barrier.