Lateral　brace　is　an　effective　way　to　increase　the　out-of-plane　stability　of　steel　arches,　and　the　certain　bracing　stiffness　achieving　full　restraining　effect　is　concerned.　Unlike　braced　columns　and　beams,　the　buckling　of　steel　arches　with　discrete　lateral　braces　and　the　effect　of　bracing　stiffness　are　not　well　explored.　This　paper　deals　with　the　bracing　stiffness　effect　of　equally-spaced　lateral　translational　braces　and　rotational　braces　in　steel　circular　arches　pertaining　to　elastic　out-of-plane　flexural-torsional　buckling.　Firstly,　for　arches　with　discrete　lateral　translational　braces　in　uniform　compression,　an　analytical　solution　for　the　threshold　bracing　stiffness　is　derived　by　the　Rayleigh-Ritz　method,　ensuring　full　restraint　of　the　displacement　at　the　bracing　points.　Then　for　arches　with　discrete　rotational　braces　in　uniform　compression,　the　flexural-torsional　buckling　modes　are　explored　using　the　finite　element　analysis　(FEA),　then　improved　predictions　to　the　buckling　load　related　to　the　bracing　stiffness　are　obtained　theoretically　by　assuming　proper　buckling　shapes.　Compared　with　the　FEA　results,　it　is　found　that　the　analytical　solutions　of　threshold　stiffness　proposed　for　arches　in　uniform　compression　are　reasonably　accurate　and　can　be　used　in　other　loading　cases　for　arches　under　combined　compression　and　bending　moment　conservatively.