In this paper the nonlinear problem of the free boundary equilibrium of a plasma inside a conducting circular shell has been solved analytically in the high beta limit. The unknown function describing the plasma shape has been expanded in a Volterra functional series, the functional analogous to the Taylor series. The hierarchy of the linear integral equations obtained from the expansion is, at least in principle, analytically solvable, so that the solution of each equation can be given in a closed form. The analytical computations have been carried out up to the fourth order and the results compared with numerical computations.