Western countries are increasingly demanding for robust structures, i.e., structures capable of withstanding local damage caused by unforeseen extreme events without triggering a progressive collapse, thus reducing the magnitude and proportion of the resulting consequences.In this paper, the robustness of framed RC buildings is analysed by comparing the reliability of the damaged structure with that of the original structure and considering (or not) the contribution of the masonry infill walls. To validate the adopted methodology, this is tested on a residential RC building severely damage due to a landslide, herein considered as case-study. A numerical model of the original, as well as, of the damaged structure is defined using force-based finite elements with distributed plasticity. Masonry infill walls are modelled as equivalent internal struts. Monte Carlo simulation and FORM coupled with artificial neural networks and response surface polynomials are used in parallel to perform the reliability analyses of both original and damaged structures. Obtained results show that the masonry infill walls are fundamental to contain damage progression after the failure of a couple of columns. In fact, without these non-structural elements, the structure would lack in robustness, and the probability of failure would be above 99%. On the contrary, by considering the structural contribution of the masonry infill walls, the robustness of the structure would be circa of 30% corresponding to a failure probability of 6%.