The exact solution to the nonlinear problem of the buckling of a shallow, circular arch subjected to a uniform pressure or a concentrated load is given. In addition an explicit bifurcated equilibrium path is presented. The buckling loads, according to several criteria, are found and their range of validity is investigated in detail. It is shown that even if the smallest buckling load is associated with an asymmetric bifurcation this alone is not a sufficient condition for the asymmetric buckling criterion to govern the problem.