An analytical method is described to extend an existing equilibrium model of a straight cylindrical plasma column with elliptic cross-section, traversed by a uniform axial current, and surrounded by a vacuum. This model is the zero order in a procedure in which the ideal MHD equations are linearized after the introduction of small perturbations which represent toroidicity, deviation from ellipticity and external force-free currents. The solution of the resulting equations is used to analyse the effects of the perturbations, major effects being the shift of stagnation points and reshaping of the outer flux surfaces. Numerical examples are given and a comparison is made with other existing theories and with belt screw-pinch experiments.