At the time of the Voyager 2 flyby of Uranus, the rotational axis of the planet will be roughly antiparallel to the solar wind flow. If Uranus has a magnetic dipole moment that is approximately aligned with its spin axis, we will have the rare opportunity to observe a ''pole-on'' magnetosphere as discussed qualitatively by Siscoe(1971). Due to the axial symmetry of a pole-on magnetosphere we are able to utilize the Grad-Shafranov theory for calculating a self-consistent magneto-hydrostatic equilibrium model of the magnetosphere of Uranus. In this paper we present an analytic model for the linear case. We also mention an approximation method which enables us to calculate the tail configuration when different relations between the thermal plasma pressure and the vector potential are assumed.