We consider the interaction of Alfven waves with the auroral acceleration region (AAR), which is characterized by a mirror resistance and a related electric potential drop that supports a field-aligned upward current and the acceleration of electrons. An Alfven wave incident on the AAR from the magnetosphere partially reflects back and partially penetrates into the AAR. An analytical treatment of the interaction of Alfven waves with the combined magnetosphere-AAR-topside ionosphere-E layer system immersed into a converging dipole-like magnetic field has been made within the thin AAR approximation. The rate of wave reflection/transmission is estimated to be critically dependent on the wave transverse scale. Incident Alfven waves with spatial scales about the Alfven damping scale λA are absorbed most effectively in the AAR. Magnetospheric Alfven waves penetrating into the AAR can produce oscillatory variations of the field-aligned potential drop and field-aligned electron acceleration. Modeling the spatial spectrum of an Alfven burst by a power-law dependence $propto$ k-p in the interval between low and high cutoff wave numbers indicates that the estimated rate of total wave power absorbed by the AAR is significant, up to 30--50% depending on p, when the ionospheric projection of the low cutoff wave number is on the order of the scale λA.