The gravity field for asteroid 433 Eros has been determined in terms of ellipsoidal harmonic functions by processing the Doppler tracking data of the NEAR spacecraft while it was in orbit about the asteroid. Using the same set of NEAR spacecraft Doppler tracking data, comparative descriptions of the Eros gravity field are provided for both the ellipsoidal and the traditional spherical harmonic models. It is shown that for elongated bodies, like the asteroid Eros, the ellipsoidal harmonics model permits a better representation of the gravity signature than does the spherical harmonics model. Eros has a nearly uniform density but there are negative gravity anomalies near the ends of Eros and positive gravity anomalies near the Psyche crater and the Himeros depression.