The possibility that electrons could be accelerated by inertial Alfvén waves to hard X-ray-emitting energies in the low solar corona during flares is investigated theoretically. This investigation is prompted in part by recent microwave observations indicating that the coronal magnetic field is strong enough that the Alfvén velocity c A above active regions could be of the order of a tenth of the speed of light or more; electrons can be accelerated to velocities in excess of c A on collisionless timescales via reflection by a single inertial Alfvén wave pulse. It is shown that the fraction of particles accelerated is a sensitive function of the initial electron temperature and the transverse length scale dx of the shear Alfvén wave pulse; under typical pre-flare coronal conditions, a significant fraction of the electron population can be accelerated if dx is of the order of a few metres or less.