Because a three-pinned circular arch is statically determinate, when it is subjected to a uniform radial load q, linear in-plane analysis has shown that the uniform load will produce quite simple internal actions: a uniform axial compressive force N = qR and zero-bending moment, where R is the radius of the arch. This is consistent with equations in textbooks for structural mechanics. However, the non-linear behavior and buckling of three-pinned arches are very different from their linear counterparts. The uniform radial load can produce significant bending moments in the three-pinned arches, and the value of the uniform axial compressive force in the three-pinned arches is greater than qR. In addition, it is also shown in this paper that the solutions for the in-plane elastic buckling load of three-pinned arches available in the open literature cannot predict their in-plane buckling loads correctly.