The kinetics of an ideal controlled ＇living＇ free radical polymerization (LFRP) are studied using a combination of analytic and numeric methods. It is shown that the ideal LFRP kinetics are characterized by the fast capping/uncapping reactions and the slow propagation of polymer radicals. The polymerization rate is determined by the rate of initiation, monomer and free capping agent concentrations, as well as, the rate of capping/uncapping. The molecular weight is shown to be a linear function of conversion, and the ultimate molecular weight is determined by the initial monomer to initiator concentration ratio. The polydispersity is determined by the ultimate molecular weight and polymerization rate.