This paper deals with analytical modelling of inelastic local flange buckling of compressed I-beam flanges. A short discussion of the relevance of different constitutive models for the inelastic material behaviour is carried out. It is claimed that what is known as the `plastic buckling paradox' is not at all a paradox but a result of improper use of plasticity theory. An analytical model for the inelastic local buckling of an I-beam flange is proposed. The model considers the buckling process as being composed of two pans. The first is associated with inelastic torsional buckling of a compressed flange and the second part corresponds to a yield line plate buckling configuration which includes the effect of stress redistribution due to large deformations. The transition between these phases is left out in the model. The model is capable of predicting approximately the force-deformation relation of a locally buckling stocky flange for different stress-strain relations. The model is evaluated against experiments and the agreement is found quite reasonable.