Abstract: Based on the total potential energy of elastic curved beams by considering the geometrical nonlinearity, the theoretic solution for the flexural-torsional buckling load of fixed-end circular arches subjected to uniform compression and bending is deduced with the Retz method, taking the effects of warping rigidity into account. Under the uniform radial load, flexural-torsional buckling load of fixed-end circular arches decreases as the subtended angle increases, which is different from simply supported arches. Besides, the critical load of fixed-end circular arches has the non-trival solution at the subtended angle of 180°. Either positive or negative bending moments, could lead the flexural-torsional buckling load of fixed-end circular arches to increase as the subtended angle increases. Numerical examples are presented and compared with other researcher’s results. The equations obtained are verified.