This paper investigates the in-plane inelastic buckling of high strength steel (HSS) circular arches with pinned or fixed end supports. A finite element (FE) model is developed to analyse in plane behaviour and buckling loads of HSS circular arches under general loading conditions which considers geometric non-linearity, material inelasticity, initial imperfection and residual stresses of welded HSS I-sections. The FE model is validated by comparison to analytical elastic buckling loads for arches in uniform compression, and experimental results reported in the literature on the out-of-plane elastic-plastic buckling of steel arches. It is found that current design codes for normal strength steel (NSS) structures require modification before application to HSS arches. Based on the results of the FE analysis, design equations are proposed which are in-line with existing provisions for NSS structures for both fixed and pin-ended arches under uniform compression and combined compressive and bending actions. The presented design rules give good lower-bound predictions for in-plane buckling strength of fixed and pinned HSS arches. Additionally, the influence of residual stresses and size of initial geometric imperfections on in-plane buckling strength are explored.