Until recently, most asteroids were thought to be solid bodies whose shapes were determined largely by collisions with other asteroids. Recent work by Burns and others has shown that many asteroids may be little more than rubble piles, held together by self-gravity ; this means that their shapes may be strongly distorted by tides during close encounters with planets. Here we report on numerical simulations of encounters between an ellipsoid-shaped rubble-pile asteroid and Earth. After an encounter, many of the simulated asteroids develop the same rotation rate and distinctive shape as 1620 Geographos (i.e., highly elongated with a single convex side, tapered ends, and small protuberances swept back against the rotation direction). Since our numerical studies show that these events occur with some frequency, we suggest that Geographos may be a tidally distorted object. In addition, our work shows that 433 Eros, which will be visited by the NEAR spacecraft in 1999, is much like Geographos, suggesting that it too may have been molded by tides in the past.