A Radon transform mapping is developed which allows correct migration below plane sloping layers to be achieved. The mapping, which is the P-tau equivalent of a Fourier transform mapping, consists of p shifting and weighting. The effect of the mapping is to move the recording plane to a sloping interface. Migration then becomes conventional migration in a horizontally layered medium. Breaking the process into a sequence of steps gives a high level of insight into this particular wave-field-extrapolation problem. Applying the Radon transform mapping to a synthetic example of migration below a sloping layer produces excellent results. However, the method is accurate only for planar reflectors.