Abstract A new, physically motivated, continuous microslip model of friction is developed for analyzing the dynamic response of frictionally damped structures in which the friction interface is subjected to high normal loads. By using this model with a single-degree-of-freedom oscillator it is found that incorporating the effects of partial slip of the friction interface can result in significant reductions of the resonant response with respect to that of a system in which only gross slip is allowed. Comparisons with experimental results are presented in a companion paper [1].