A computer program has been written which employs an implicit Euler method to solve directly the complete set of coupled differential equations which result from an analysis of polymerization kinetics. The program was written to make full use of the speed and power of modern supercomputers, and is suited to the solution of very large stiff systems of differential equations. The benefit of treating each propagation step as a discrete reaction is that information on the evolution of the molecular weight distribution is obtained directly without the need to make perhaps unjustified assumptions such as the steady-state approximation. For illustrative purposes, the method has been applied in the kinetic simulation of 'quasi-living' radical polymerization to assess the effect of experimental variables on the molecular weight, molecular weight distribution, and rate of polymerization. The calculations show that 'quasi-living' radical polymerization can produce polymers with polydispersities approaching those obtained with anionic 'living' polymerizations. Some necessary conditions for the formation of polymers with narrow molecular weight distribution are defined.