The semi-analytical complex finite strip method is used to study the elastic local buckling of composite tee-section beams in negative moment and shear which contain a longitudinal stiffener attached to the web. The optimum position of this stiffener for different positions of the neutral axis is calculated in order to maximize the local buckling stress. Design graphs for longitudinal stiffeners are presented. Interaction curves between shear and bending for different positions of the neutral axis in a stiffened girder are given. Key words: composite beams, elasticity, finite strips, local buckling, longitudinal stiffeners, webs.