We have developed a new data-driven algorithm that uses directional elastic wave packets as seismic sources to image subsurface voids (i.e., cavities). Compared to a point source, the advantage of the new approach is that the wave packet illuminates only a small volume of the medium around the raypath to significantly reduce multiple scattering effects in the imaging. We take the difference of traces at identical source-receiver offsets from each of two neighboring source packets. The difference mainly contains the void scattering events but not the direct waves, the layer reflections, refractions, nor layer-related multiples. We use 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 wave packet can be numerically synthesized using existing shot gathers; therefore, no special physical source is required. We determine 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 test the robustness of our method using the same data but with 15% root-mean-square random noise added. Furthermore, we compare our method with the reverse time migration 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.