The asteroid (16) Psyche, target of NASA's “Psyche” mission, is thought to be one of the most massive exposed iron cores in the solar system. Earth‐based observations suggest that Psyche has a metal‐rich surface; however, its internal structure cannot be determined from ground‐based observations. Here we simulate impacts into a variety of possible target structures on Psyche and show the possible diversity in crater morphologies that the “Psyche” mission could encounter. If Psyche's interior is homogeneous, then the mission will find simple bowl‐shaped craters, with a depth‐diameter ratio diagnostic of rock or iron. Craters will be much deeper than those on other visited asteroids and possess much more spectacular rims if the surface is dominated by metallic iron. On the other hand, if Psyche has a layered structure, the spacecraft could find craters with more complex morphologies, such as concentric or flat‐floored craters. Furthermore, if ferrovolcanism occurred on Psyche, then the morphology of craters less than 2 km in diameter could be even more exotic. Based on three to four proposed large craters on Psyche's surface, model size‐frequency distributions suggest that if Psyche is indeed an exposed iron core, then the spacecraft will encounter a very old and evolved surface, that would be 4.5 Gyr old. For a rocky surface, then Psyche could be at least 3 Gyr old.