The present study deals with a numerical approach for the seismic response of existing industrial reinforced concrete (RC) structures, which are elements of the recent built Cultural Heritage. These RC structures have been damaged due to extreme environmental actions and are to be seismically upgraded by using cable elements (tension-ties). Special attention is given to flexure-shear failure effects. A double discretization, in space by the Finite Element Method and in time by a direct incremental approach, is used. The unilateral behaviour of the cable-elements, which can undertake tension stresses only, is strictly considered and results to inequality constitutive conditions. Finally, using damage indices, the optimal strengthening version of cable-systems is chosen for the case of multi-storey RC frames under seismic sequences of multiple earthquakes. KEY WORDS: Computational Structural Mechanics, Seismic Upgrading of Historic RC Structures, Strengthening by Cable-braced Systems, Flexure-Shear failure effects, Multiple Earthquakes.