In the present paper, the coupled behavior of structural systems obtained by connecting a moment resisting frame structure with a vertical elastic truss, known in the literature as strong-back, which acts as a mast by imposing to the structure a given lateral deformed shape, is investigated. The rigid behavior of the strong-back, which is designed in order to remain in the elastic field under strong seismic ground motion, imposes a uniform inter storey drift along the frame height, thus avoiding undesired effects such as soft storey and weak storey mechanisms.Consequently, the whole structural system may be, at first approximation, modelled as an equivalent Single Degree of Freedom system thus allowing for an analytical description of its response. In particular, in the work the attention is paid to the mutual actions exchanged by the strong-back and the frame by solving the static equilibrium equations, assuming a shear type behavior for the frame. Finally, some numerical simulations of frame systems with strong-back systems as subjected to earthquake ground motions are developed, encompassing both shear type frames and frames with flexible beams.