A novel friction damping system for the aseismic design of framed buildings has been proposed by Canadian researchers. The system has been shown experimentally to perform very well and is an exciting development in earthquake resistant design.The design of a building equipped with the friction damping system is achieved by determining the optimum slip load distribution to minimize structural response. The optimum slip load distribution is usually determined using the general nonlinear dynamic computer program DRAIN-2D, which requires extensive computer time and is not practical for most design offices.This paper describes a new, efficient, numerical modelling approach for the design of friction damped braced frames. The hysteretic properties of the friction devices are derived theoretically and included in a friction damped braced frame analysis program, which is adaptable to a microcomputer environment. The optimum slip load distribution is determined by minimizing a relative performance index derived from energy concepts. The new numerical approach is much more economical to use than DRAIN-2D and is of great value for the practical design of friction damped braced frames. Key words: braced frames, brake lining, performance index, damping, dynamics, earthquakes, energy, friction.