Harris <1962> developed a one-dimensional current sheet model in a magnetic field that was self-consistent with a collisionless Maxwellian plasma. This model has served as a starting point for many current sheet studies. Kan <1973> showed how this approach could be extended to two dimensions, but there has been little further application of this extension to magnetospheric problems. We have followed Kan's technique and give exact analytic expressions for plasma and magnetic field structures in the vicinity of a two-dimensional magnetic X point. The plasma is Maxwellian with arbitrary electron to ion mass ratio, but in the present stage of work the flow is constrained to be perpendicular to the plane containing the X point. The model is flexible in that it contains parameters that should allow it to be adapted to particular observational geometries and to be extended further using perturbation techniques to higher dimensions.