Separations of up- and down-going as well as of P- and S-waves are often a part of processing of multicomponent recorded data and propagating wavefields. Most previous methods for separating up/down propagating wavefields are expensive because of the requirement to save time steps to perform Fourier transforms over time. An alternate approach for separation of up-and down-going waves, based on extrapolation of complex data traces is extended from acoustic to elastic, and combined with P- and S-wave decomposition by decoupled propagation. This preserves all the information in the original data and eliminates the need for a Fourier transform over time, thereby significantly reducing the storage cost and improving computational efficiency. Wavefield decomposition is applied to synthetic elastic VSP data and propagating wavefield snapshots. Poynting vectors obtained from the particle velocity and stress fields after P/S and up/down decompositions are much more accurate than those without because interference between the corresponding wavefronts is significantly reduced. Elastic reverse time migration with the P/S and up/down decompositions indicated significant improvement compared with those without decompositions, when applied to elastic data from a portion of the Marmousi2 model.