This paper provides a methodology to quantify the Influence of masonry infill walls topology on the structural damage of a steel frame building suffer from seismic events. Initially, several artificial accelerograms, compatible with the design spectrum of the Greek Antiseismic Code, have been composed. The seismic intensity parameters that have been evaluated were the peak ground acceleration (PGA), the Arias intensity, the strong motion duration (SMD) as defined by Trifunac/Brady (SMDTB), byTrifunac/Novikova (SMDTN) and by McCann (SMDMC), the seismic power based on used the definitions of SMD (PTB, PTN, PMC) and the root mean square seismic acceleration (RMS). The presented methodology is applied on a steel frame designed according to the rules of the recent Eurocode for steel structures EC3 and the Greek Antiseismic Code, respectively. In addition, the initial bare frame has been examined having 4 different layouts of infill walls on it, resulting into 5 different frame types. Nonlinear dynamic analyses have been carried out in order to evaluate the structures’ seismic response. For this purpose the computer program IDARC has been used. Among the several structural response characteristics, the focus is on the overall structure damage indices (OSDI). These have been expressed by the OSDI after Park/Ang and by the maximum inter-storeydrift ratio (MISDR). As the numerical results have shown infill walls proved to have a very positive contribution in the structure’s seismic response giving us an average of 80.11% reduction of the mean DI after Park/Ang in the non-zero values of the same DI between the bare frame structure and its infill wall reinforced counterpart. Similar results have been observed for the MISDR as well, where an approximate 60.79% average reduction has been noted. Finally, a statistical study provided strong correlation between the examined damage indices and the Arias intensity, the seismic power and the RMS. On the other hand, medium correlation between the damage indices and the PGA, and low correlation was observed between the damage indices and the strong motion duration for all the frame types.