During time, the equilibrium state of a steel-concrete mixed beam progresses under the concrete shrinkage. In this context, a contribution to the search of the time-dependant behaviour of mixed beams, including the shrinkage phenomenon of the concrete slab, is dealt with in this paper. The influence of the concrete shrinkage, taking into account the slab reinforcement contribution, on the strength of the mixed beams is taken into account using the linear concrete viscoelasticity theory. With the help of this theory we obtain an analytic model, based on two linear differential equations that result in the over-time-behaviour of the steel-concrete mixed beams. From this model we can determine, at any time t, the values of the normal force and bending moment due to the concrete shrinkage. So it allows us to give an account of the stress state evolution developed in the cross sections of the steel-concrete mixed beams. The results obtained from the application of the suggested model are completely comparable with the results derived by the method proposed by EUROCODE 4