Based on the generalized Maxwell-model, a viscoelastic material approach for steady-state rolling structures has been developed. Unlike a transient finite element formulation the final state is attained in a few load increments and just one time step. The consistent linearization of the steady-state viscoelastic constitutive formulation leads to additional coupling matrices so that the number of non-zero entries in the global stiffness matrix is increased. The steady-state formulation of the viscoelastic material approach as well as the transient formulation allow the addition of so-called Prandtl-elements to consider elastoplastic effects, too. Numerical results confirm the robustness, reliability and capability of the steady-state viscoelastic material formulation.