This work proposes a technique based on the phase-shift method to implement pre-stack depth migration on locally transverse isotropic media (LTI), in which the direction of the symmetry axis varies continually along the layers. Through numerical seismic data simulations the methods robustness and stability were tested in relation to the axis symmetry variations. For seismic modeling, a generalization of the finite differences method for the solution of the elastic wave equation was used. With this procedure, it was possible to accommodate seismic modeling on LTI media defined by six parameters at each grid point, i.e., density, P and S wave propagation velocities along the local symmetry axis, Thomsen parameters and, the direction of the local symmetry axis itself. In order to separate from the seismograms the qP and qSV wavefields, an algorithm based on the Christoffel equation was implemented. The migration for each common shot gather is implemented solely by phase-shift based algorithms, which means that not only the depropagation of the registered wavefield, but also the generation of the time matrices involved in the imaging condition were obtained in this manner for each set of parameters at each depth level. The migration results using qP-qP and qP-qSV reflections show that the horizons were located precisely, and that the process is stable in relation to the symmetry axis variations. The proposed method is not restricted to multicomponent seismic acquisitions, but it can be applied to marine seismic data using streamers, or Ocean Bottom Cables or vertical cables. Since the proposed method uses phaseshift algorithms, its parallel implementation can be highly efficient.