The behaviour and modelling of circular sections confined by Fibre Reinforced Polymer (FRP) reinforcement have been examined extensively recently. This study concentrates on FRP confined specimens with square sections under axial loading. An experimental programme was designed in which 101 prismatic concrete specimens of different strengths were tested. The specimens had dimensions of 200×200×320 mm. They were externally confined by carbon or glass FRP sheets in different confinement volumetric ratios. Monotonic as well as cyclic axial compressive loads were applied. The testing results indicate that square concrete sections, properly confined by FRP reinforcement, can achieve high levels of strength and ductility. It was found that glass FRP is less effective in terms of strength and ductility enhancement when compared with carbon FRP confinement of same axial rigidity for low volumetric ratios. A plasticity model capable of reproducing hardening–softening behaviour is also presented here to predict the response of the FRP confined specimens. The model generates the stress–strain curves for axially loaded square columns confined by FRP sheets or tubes. The predicted curves are compared successfully to the present as well as other published experimental data.