Employing the vector processing of multicomponent seismic data, elastic Kirchhoff migration is used to conduct a multicomponent joint migration velocity analysis (MVA) of PP- and PS-waves in the angle domain. In vector-wavefield imaging, the elastic imaging condition has been extended to nonzero time and space shifts. We apply the extended imaging condition to elastic Kirchhoff migration to extract angle-domain common-image gathers (ADCIGs) of PP- and PS-waves. This method, which is derived from 3D wave propagation theory, directly operates on the vector wavefields and automatically resolves the problem of PS-wave polarity reversal in the migration sections. Based on the kinematic characteristics of PP- and PS-waves in the incident-angle domain, the velocity updating functions for P- and S-waves are derived. By combining the ADCIGs flatness criterion and the PP- and PS-wave image-depth consistency principle, the accuracy of P- and S-wave velocities can be assessed. The method was tested on a 2D thin-interbed model and the 2D Marmousi2 model. We found that the proposed method extracts the PP- and PS-wave ADCIGs effectively and produces appropriate P- and S-wave velocity fields. This method can be applied to time-delay gathers and to vertical or inline gathers in the 3D case.