The reflected P- and S-waves in a prestack 3D, three-component elastic seismic section can be separated by taking the divergence and curl during finite-difference extrapolation. The elastic seismic data are downward extrapolated from the receiver locations into a homogeneous elastic computational model using the 3D elastic wave equation. During downward extrapolation, divergence (a scalar) and curl (a three-component vector) of the wavefield are computed and recorded independently, at a fixed depth, as a one-component seismogram and a three-component seismogram, respectively. The P- and S-velocities in the elastic computational model are then split into two independent models. The divergence seismogram (containing P-waves only) is then upward extrapolated (using the scalar wave equation) through the P-velocity model to the original receiver locations at the surface to obtain the separated P-waves. The x-component, y-component, and z-component seismograms of the curl (containing S-waves only) are upward extrapolated independently (using the scalar wave equation) through the S-velocity model to the original receiver locations at the surface to obtain the separated S-waves. Tests are successful on synthetic seismograms computed for simple laterally heterogeneous 2D models with a 3D recording geometry even if the velocities used in the extrapolations are not accurate.