This article deals with the behavior under service loads of thin-walled, precast, prestressed beams that are frequently used to build floors and roofs of shopping centers, industrial buildings, and warehouses. Because of the dissymmetric shape, their dead load gives rise to torsion, to which the beam reacts according to Vlasov's theory. This work applies Vlasov's theory to a heterogeneous beam made with a homogenous linear viscoelastic material ( i.e., concrete) and a linear elastic one ( i.e., the reinforcement). The beam is subjected to long-term bending and torsional moments, and the solving system takes into account the noncompatible strains imposed between the two materials ( i.e., prestressing). (C) 2016 American Society of Civil Engineers.