Our computer simulations show that when a small asteroid flies by Earth, seismic shaking can be induced. For the asteroid Apophis, its 2029 encounter with Earth may induce seismicity that will cause wide-spread resurfacing of its regolith. We consider how different plausible interior structures for Apophis may lead to different magnitudes of seismic shaking and resurfacing. We then extend our results for the possible close encounter of the asteroid 2024 YR4 with the Moon in 2032.