A spherical harmonic model of the planetary magnetic field of Uranus is obtained from the Voyager 2 encounter observations using generalized inverse techniques which allow partial solutions to complex (underdetermined) problems. The Goddard Space Flight Center ''Q3'' model is characterized by a large dipole tilt (58.6¿) relative to the rotation axis, a dipole moment of 0.228 G RU3, and an unusually large quadrupole moment. Characteristics of this complex model magnetic field are illustrated using contour maps of the field on the planet's surface and discussed in the context of possible dynamo generation in the relatively poorly conducting ''ice'' mantle. ¿ American Geophysical Union 1987