The subject of acoustic radiation pressure on a gas bubble is important in many applications because it controls how bubbles are moved by acoustic fields to target locations, and often how they act upon the target. Previous theoretical treatments assume a spherical bubble undergoing linear pulsations, but some (such as cleaning using Faraday waves on the bubble wall) require that the bubble be aspherical. Therefore, this paper derives ways to calculate the variation in the radiation pressure due to the non-spherical bubble oscillations. The magnitude and direction of the radiation force are determined by two factors: the amplitude of volume oscillations, V, and the phase relationship between those oscillations and the acoustic field which drives them. There are two key findings that correct for the predictions of a model accounting for only linear pulsations. First, the growth of the radiation force slows down as V ceases to increase linearly with increasing amplitude of the acoustic wave above the threshold. Second, although both models show that the direction of the force relative of the standing wave antinode can be attractive or repulsive depending on frequency, when distortion modes are included the frequency at which this force changes its sign is shifted.