Unanchored nonstructural elements are often extremely sensitive to seismic actions, and in many cases, their seismic response is governed by rocking motion. Rocking activation is often associated with low-intensity seismic actions, and even moderate-intensity actions might cause major damage to objects and casualties. This is even more significant in the case of critical facilities such as hospitals, which host highly valuable unanchored medical components that are of primary importance of hospital functioning and vital tasks. The paper presents a novel approach for assessing seismic capacity of rocking-dominated elements housed in buildings, based on fragility surfaces that account for building filtering and magnification effects. Incremental rigid block analysis results are processed considering (a) varied block slenderness and size, (b) various engineering demand parameters (EDPs), including ground and floor acceleration and velocity peak parameters, and (c) incremental damage states (DSs). Fitting correlations are provided for comparison purposes and expeditious estimations of statistical-based capacities. In particular, the closed-form capacity criteria allow to estimate both statistical capacity and expected uncertainty as a function of the abovementioned features, i.e., block geometry, EDP, and DSs. The study also reports an example of seismic safety assessment based on the use of the developed criteria, referring to both representative ordinary and critical buildings located in low- to high-seismicity areas in Italy.