The research leading to this paper was prompted by the need to estimate strength and stiffness of Rigid Rocking Cores (RRCs) as essential elements of resilient earthquake resisting structures. While a limited number of such studies have been reported, no general study in terms of physical properties of RRCs, their appendages and adjoining structures have been published. Despite the growing knowledge on RRCs there are no design guidelines on their applications for seismic protection of buildings. The purpose of the present article is to propose effective rigidity limits beyond which it would be unproductive to use stiffer cores and to provide basic guidelines for the preliminary design of RRCs with a view to collapse prevention, re-centering and post-earthquake repairs/replacements. Several examples supported by computer analysis have been provided to demonstrate the applications and the validity of the proposed solutions.