Buckling performance of thin metallic shells can be enhanced by external wrapping of FRP composite layers. But the effectiveness and the extent of such FRP strengthening is influenced by the buckling characteristics of the metallic shell. This paper presents a detailed numerical study to bring out the changes in buckling behaviour and buckling modes of metallic cylindrical shells of different r/t ratios, exhibiting all varieties of buckling viz. elastic, axisymmetric plastic, and asymmetric plastic, due to changes in the hoop and longitudinal stiffness of the FRP wrap. The most general buckling behaviour of the FRP strengthened shells exhibiting elastic, pre-strain localization, post strain localization, axisymmetric buckle growth, and the asymmetric buckle growth stages are being brought out. Subsequently, the influence of parameters viz. r/t ratio, modulus and yield strength of the metallic shell, and the type and magnitude of the FRP strengthening on this general buckling behaviour are analysed. The results demonstrate that 1) the elastic buckling shells display a stepwise increase in load capacity with an increase in hoop modulus of the FRP wrap; 2) for the plastic buckling shells undergoing asymmetric buckling modes, a minimal increase in longitudinal stiffness of FRP wrap, just sufficient to reach the shells’ yield capacity, would lead to an optimal design; and 3) for the plastic buckling shells failing due to axi-symmetric bulging at their ends, the increase in longitudinal stiffness of FRP, increases both the yield capacity and the pre-strain localization stiffness, leading to a large increase in buckling capacity. © 2021 Elsevier Ltd