Abstract The behaviour of a curve adhesive joints between two generic profiles is investigated. In particular, a mechanical model accounting for the curvature radius is formulated as a generalization of a previous one introduced by the same authors in recent time. The coupling between the shear/flexure and extensional equilibrium problems, the curvature radius, the energy mobilization corresponding to the most common cohesive interface laws, are introduced in order to identify the governing parameters of the joint mechanical response. A wide numerical investigation has been developed in order to evaluate the ultimate load and the effective stress transfer length.