Elastic, prestack, reverse‐time, finite‐difference migration of two‐component seismic surface data requires data extrapolation and application of an imaging condition. Data extrapolation involves synchronous driving of the vertical‐component and horizontal‐component finite‐difference meshes with the time reverse of the recorded vertical and horizontal traces, respectively. Extrapolation uses the coupled elastic wave equation for variable velocity solved with a second‐order, explicit finite‐difference scheme. The imaging condition at any point in the grid is the one‐way traveltime from the source to that point. Elastic migrations of both synthetic test data and real two‐component common‐source gathers produce simpler images than acoustic migrations because of the coalescing of double reflections (compressional waves and shear waves) into single loci.