In bridge construction, the use of stiffened plates for box-girder or steel beams is common day to day practice. The advantages of the stiffening from the economical and mechanical points of view are unanimously recognized. For curved steel panels, however, applications are more recent and the literature on their mechanical behaviour including the influence of stiffeners is therefore limited. Their design with commercial finite element software is significantly time-consuming, which reduces the number of parameters which can be investigated in an optimization procedure. The present paper is thus dedicated to the study of the behaviour of stiffened curved panels under uniform longitudinal compression. It addresses the linear buckling and the ultimate strength which are both influenced by the coupled effects of curvature and stiffening. It finally proposes a design methodology based on that for stiffened flat plates adopted by European Standards and a column-like behaviour. •Interaction between curvature and stiffening on the shape of the buckling modes.•Reliability of EC3 model for flat panels for reduced curvature of sub-panels.•New design procedure based on a column-like behaviour for high curvatures.