A stochastic model was developed to simulate the polymerisation kinetics and the detailed microstructure of the resulting polymers made by the living radical polymerisation of styrene initiated by epoxide radical ring opening. The model was used to predict monomer conversion, average molecular weight, polydispersity index, and molecular weight distribution as a function of polymerisation time. Simulations were used to explore the effects of rate constant values on chain microstructures and polymer properties and validated with experimental data published in the literature. It was found that some parameters, such as the exchange rate constant, have no significant effect on the polymerisation kinetics, whereas major effects were observed when other rate constants, such as the reduction rate constant, were changed.