  The parametric equations of the plane curves determining the equilibrium
shapes that a uniform inextensible elastic ring or tube could take subject to a
uniform hydrostatic pressure are presented in an explicit analytic form. The
determination of the equilibrium shape of such a structure corresponding to a
given pressure is reduced to the solution of two transcendental equations. The
shapes with points of contact and the corresponding (contact) pressures are
determined by the solutions of three transcendental equations. The analytic
results presented here confirm many of the previous numerical results on this
subject but the results concerning the shapes with lines of contact reported up
to now are revised.
