This article presents a numerical study on the influence of the anchorage shear hysteresis on the seismic response of nonstructural components (NSC) connected to multi-storey reinforced concrete (RC) buildings, and of the anchorage itself. To cover a variety of different types of shear hysteresis shapes, this contribution considered the experimental results obtained for five types of post-installed anchors. The results were used for calibrating the hysteresis model of the anchorage connecting an ideal NSC with rigid fixture and a 12-storey RC building host-structure. Using a suit of 40 earthquake records and assuming a single NSC at each storey level anchored by a single fastener, a series of non-linear dynamic analyses of the structure-fastener-nonstructural system was carried out. The results showed significant differences in terms of maximum acceleration and force of the NSC and anchorage, respectively, depending on the type of anchor. These seismic demands were sometimes larger than those required by the reviewed code provisions for rigid NSC, but also for the most restrictive code-case for flexible NSC. The results presented different amounts of scatter, mostly related to the size of the annular gap and of the loading stiffness of the anchorage. It is shown that the maximum force achieved by the anchorage is directly related to the peak relative velocity of the NSC within the gap region. It was concluded that the shape of the shear hysteresis of the anchorage highly influences the response of the NSC and the anchor itself and should not be neglected in practice.