We develop a new data-driven algorithm that uses directional elastic wavepackets as seismic sources to image subsurface voids (i.e., cavities). Compared with a point source, the advantage of the new approach is that the wavepacket illuminates only a small volume of the medium around the ray path to significantly reduce multiple scattering effects in imaging. We take the difference of traces at identical source-receiver offsets from each of two neighboring source packets. The difference contains mainly the void scattering events but not the direct waves, the layer reflections, refractions, nor layer-related multiples. We use both P-to-P and P-to-S scattered waves to locate the voids and the results using scattered P and S waves can cross-validate each other to reduce the possibility of false detections. The directional wavepacket can be numerically synthesized using existing shot gathers so no special physical source is required. We demonstrate our method using data calculated using a boundary element method to model the seismic wavefield in an irregularly layered medium containing several empty voids. We show the robustness of our method using the same data but with 15% RMS random noise added. Furthermore, we compare our method with the RTM imaging method using the same data and find that our method provides superior results that are not dependent on the construction of a velocity model.