We determined the mass of asteroid 433 Eros, its lower order gravitational harmonics, and rotation state, using ground-based Doppler and range tracking of the Near Earth Asteroid Rendezvous (NEAR)-Shoemaker spacecraft and images of the asteroid's surface landmarks. The mass of Eros is (6.687 +/- 0.003) × 1018 grams, which, coupled with our volume estimate, implies a bulk density of 2.67 +/- 0.03 grams per cubic centimeter. The asteroid appears to have a uniform density distribution. The right ascension and declination of the rotation pole are 11.37 +/- 0.05 and 17.22 +/- 0.05 degrees, respectively, and at least over the short term, the rotation state of Eros is stable with no measurable free precession of the spin pole. Escape velocities on the surface vary from 3.1 to 17.2 meters per second. The dynamical environment of Eros suggests that it is covered with regolith and that one might expect material transport toward the deepest potential wells in the saddle and 5.5-kilometer crater regions.