The sharp‐boundary model of ideal magnetohydrodynamics is presented in a form readily applicable to axisymmetric, high‐&bgr; plasmas of arbitrary cross section. The usual vacuum region outside the plasma is replaced here by a layer of force‐free currents, and the influence of force‐free currents and cross‐sectional shaping on the critical &bgr; is studied. Specific results are given for circular, elliptical, and racetrack‐like cross sections. A new parameterq* is introduced in place of the Mercierq, and it is shown thatq*≈1 is a reasonable estimate of the toroidal current limitation due to external kink modes in high‐&bgr; plasmas with noncircular cross sections.