A 2D algorithm for angle-domain common-image gather (CIG) calculation is extended and modified to produce 3D elastic angle and azimuth CIGs. The elastic seismic data are propagated with the elastic particle displacement wave equation, and then the PP-reflected and PS-converted waves are separated by divergence and curl calculations during application of the excitation-time imaging condition. The incident angles and azimuths are calculated using source propagation directions and the reflector normals. The source propagation direction vector is computed as the spatial gradient of the incident 3C P-wavefield. The vector normal to the reflector is calculated using the Hilbert transform. Ordering the migrated images with respect to incident angles for a fixed azimuth bin, or with respect to azimuths for a fixed incident angle bin, creates angle- or azimuth-domain CIGs, respectively. Sorting the azimuth gathers by the incident angle bins causes a shift to a greater depth for too-high migration velocity and to a smaller depth for too-low migration velocity. For the sorted incident angle gathers, the velocity-dependent depth moveout is within the angle gathers and across the azimuth gathers. This method is compared with three other 3D CIG algorithms with respect to the number of calculations and their disk storage and RAM requirements; it is three to six orders of magnitude faster and requires two to three orders of magnitude less disk space. The method is successfully tested with data for a modified part of the SEG/EAGE overthrust model.