A procedure is presented for investigating the response of reinforced concrete buildings to rockfall impact. The method considers a single rock hit on the basement columns, and it includes four steps: (a) calculation of the probability of a rock impact on a member of the load-bearing system, taking into account the block size and the design of the structure; (b) evaluation of the response of one or more structural elements to the hit based on element capacity; (c) in the case of structural element failure, assessment of the robustness of the whole structural system, calculating the potential for progressive collapse; and (d) calculation of a damage index (DI), which is the ratio of structural elements that fail to the total number of structural elements. The proposed method is applied to a reinforced concrete building for a range of rockfall paths and intensities. The analysis has been carried out for a 2-m-diameter block and velocities< 3.5 m/s. The possible damage range is found to be highly variable, with DI values ranging from 0.01 to 1 depending on the impact location and block velocity.