The flexibility of the connection between steel and concrete largely influences the global behaviour of the composite beam. Therefore the way the connection is modelled is the key issue in its structural analysis. Here we present a new strain-based finite element formulation in which we consider non-linear material and contact models. The computational efficiency and accuracy of the formulation is proved with the comparison of our numerical results with the experimental results of Abdel Aziz (1986) obtained in a full-scale laboratory test. The shear connectors are assumed to follow a non-linear load-slip relationship proposed by Ollgaard et al. (1971). We introduce the notion of the generalized slip, which offers a better physical interpretation of the behaviour of the contact and gives an additional material slip parameter. An excellent agreement of experimental and numerical results is obtained, using only a few finite elements. This demonstrates that the present numerical approach is appropriate for the evaluation of behaviour of planar composite beams and perfect for practical calculations.