ABSTRACT Recently, experimental studies on failure conditions of buildings equipped with curved surface sliding isolators have shown that when no displacement restraining elements are employed and the concave plates feature a flat rim, the inner slider can run on the edge of the sliding surfaces producing lateral displacement larger than the nominal isolator capacity. The over-stroke displacement capacity reduces the probability of seismic collapse of code-conforming base-isolated buildings for earthquake stronger than the design one. In order to quantify the benefit of the over-stroke displacement capacity of double concave curved surface slider (DCCSS) bearings on the seismic fragility of base isolated buildings, four case studies of six-storey reinforced concrete framed structures, consisting of new constructions and retrofit of existing structures located in high and medium hazard seismic sites, have been investigated in this paper. In all cases, two configurations of the isolation system have been considered, with end-stop displacement or with over-stroke displacement capacity. The seismic performance of the buildings has been investigated by multi-stripe nonlinear time-history analysis. The results of the nonlinear dynamic analysis at the collapse limit state have been compared with nonlinear static analysis in terms of maximum displacement and corresponding base shear. Fragility curves highlight a higher safety margin against collapse for seismic intensities beyond the design limit state of the isolation system with over-stroke capacity.