The buckling behavior of two-hinged circular arches with any height-to-span ratio is studied by formulating the problem as a two-point boundary-value problem consisting of six nonlinear, first-order differential equations and appropriate boundry conditions. The theory is exact in the sense that no restrictions are placed on the size of the deflections or on the thickness of the arch. It is approximate in the sense that plane sections are assumed to remain plane, shear deformation is neglected, and the geometric properties of each cross section are assumed to remain constant during the deflection. The problem is solved on a digital computer by a shooting method that uses two levels of regula falsi and one of iteration. Selected results as plotted by the computer are shown and interpreted.