Abstract: The differential equations of stability are derived by the principle of variation for arbitrary thin-walled curved beams. When mono-symmetric arch is subjected to uniformly distributed radial load (uniform compression) or to equal but opposite end moments (uniform bending), its in-plane displacements are uncoupled with out-plane displacements, so it undergoes either in-plane flexural buckling or out-plane flexural-torsional buckling. Theoretic solutions are obtained for mono-symmetric circular arches under uniform compression and under uniform bending respectively. The equations are simple enough to be applied in engineering. Numerical examples are presented to validate the equation, observing good agreement with the result calculated by finite element software ANSYS and previous theoretical.