Stability limits for the ideal internal kink mode are calculated analytically for the Shafranov current profile using the large aspect ratio expansion. For equilibria with q(a)>2 and circular cross section, the maximum stable poloidal beta is below 0.1. In the absence of a conducting wall, an equilibrium with q(a)<2 is unstable at arbitrarily small positive poloidal beta or shear inside the q = 1 surface. The effects of non-circularity are discussed and quantitative results are given for elliptic cross sections. (author) 2 figs., 10 refs.