An analytical approach is made to the problem of describing the toroidal equilibrium of a finite beta plasma column in the hydromagnetic approximation. The thickness of the sheath region separating the plasma from the external magnetic field is assumed to be negligibly small compared to all other dimensions (the "thin skin" approximation). The deviations of this interface from toroidal cylindrical shape are treated by perturbation theory, a procedure which is consistent with the usual series expansion in powers of reciprocal aspect ratio. The formalism provides analytic expressions for the auxiliary currents necessary to produce equilibrium in toroidal theta pinch systems such as Scyllac.