This paper presents an analytical and numerical formulation for the short- and long-term analysis of composite beams with longitudinal and vertical partial interaction in which the interface connection deforms both longitudinally, i.e. along the beam length, and vertically, i.e. transverse to the connection interface. The concrete behaviour is time-dependent and its stress-strain relationship is described by means of the integral-type creep law while the steel of the joist, the reinforcement and the shear connection are assumed to behave in a linearelastic fashion. The theoretical model is derived from the principle of virtual work. Due to the complexity of the problem, a numerical solution is then proposed. This solution requires the use of two discretisations, one in the time domain and one along the member axis. For the former one, the integral-type creep law describing the concrete behaviour is approximated based on the step-by-step procedure applying the trapezoidal rule while the spatial approximation is achieved by means of the finite element method. In this sense, a 14dof finite element is derived based on the weak form of the problem.