Although prestressing is a technique usually linked to reinforced concrete structures, composite steel-concrete beams may improve their mechanical behaviour through post-tensioning tendons. A particular feature of composite beams is the possibility of slip or partial interaction between the components as a result of the shear connection flexibility. This paper describes the development, implementation and test of a one-dimensional finite element formulation for the nonlinear analysis of steel-concrete composite beams prestressed by external tendons, fixed at discrete points along the steel component, taking into account the partial interaction between steel and concrete. Physical and geometrical nonlinearities are considered and a consistent derivation of the tangent stiffness matrix for the tendon is introduced. A recently developed procedure for state determination after prestressing operation is adapted for partially connected composite beams prestressed by external tendons. The accuracy and robustness of the finite element formulation is assessed by means of the comparison with a comprehensive series of experimental results.