This paper presents a model for the strength of inclined screws used as shear connectors in timber and concrete composite floors. Experiments show that both the stiffness and strength of screwed timber to concrete shear connections can be increased if the screws are inclined in the direction of shear; this model predicts the enhanced strength. The model is an upper bound plastic collapse model that assumes that the timber and screws behave perfectly plastically and that the concrete remains undamaged. Six failure modes are considered: yield of the screw, in tension or shear, and four modes which combine bending of the screw and timber. The four combined modes allow screw withdrawal, lateral crushing of the timber and the development of plastic hinges in the screw. A design chart is proposed which shows the expected strength and failure mode. The model is validated by comparison to two sets of experimental tests.