Abstract This paper investigates a new seismic rehabilitation technology for low-rise and mid-rise steel Concentrically Braced Frames (CBFs) vulnerable to inter-story drift concentration and soft-story failures. The technology consists of installation of a single or multiple sufficient Rocking Cores (RCs) pinned to the foundation and connected to an existing deficient multi-story CBF building to re-distribute seismic forces along its height and create more uniform inter-story drift and ductility demand distributions. Two benchmark steel CBF buildings including one three-story and one six-story are rehabilitated using the RC technology. Nonlinear static pushover analyses are conducted to demonstrate the beneficial contribution of the RC in mitigating non-uniform inter-story drift distributions in the benchmark buildings. The RC stiffness is varied and the Monte-Carlo simulation technique is adopted to generate random lateral force distributions in the nonlinear static pushover analyses. It is shown that the RC is effective in reducing inter-story drift concentration in both benchmark buildings when they reach the inter-story drift limits associated with collapse prevention, lift safety and immediate occupancy per FEMA 356. This paper also presents the strength demands on RC and the links connecting RC to existing frame from the nonlinear static pushover analyses, which are essentially caused by the first mode responses of the rehabilitated systems.