In this paper, the stability behaviour of longitudinally stiffened, transversally curved steel plates under uniform compressive stresses is investigated and new design guidelines are proposed to extend the scope of the current European standards for flat plated structures to stiffened curved plates. For this purpose, a numerical model is built in Abaqus, which is verified with own test results and numerical results from the literature. It incorporates geometric imperfections based on the modification of node coordinates using sinusoidal functions, and is further used in a comprehensive parametric study based on nonlinear numerical analysis (GMNIA). The parametric study investigates the effects of curvature, slenderness of the plate, size of stiffeners and shape of initial imperfections on the ultimate resistance of the stiffened curved plates. From the results, some important conclusions are drawn regarding the structural behaviour and the positive effects of curvature on the cross‐sectional resistance. In particular, it is found that stiffened curved plates are less sensitive to the shape of the initial imperfections compared to flat stiffened plates, and the introduction of curvature generally adds a reserve of resistance to the stiffened panel under compressive stresses. Based on numerical results, design rules are proposed for longitudinally stiffened curved plates subjected to compressive stresses. The rules are in accordance with the formalism of EN 1993‐1‐5 for flat plated structures and follow the effective width concept. The maximum loads obtained from numerical analysis are compared with the new design rules and a good correlation is obtained.