Stereolithography (SL) is a method which produces any object of complex geometry with desired qualities from its computer aided design and the production is realized by the free-radical photopolymerization reaction. The photopolymerization as the fundamental process of SL production is not yet well understood. The main purpose of this study is to develop mathematical models to contribute to the understanding of the reaction kinetics of the photopolymerization process and to make reliable simulations of the process. The first model was developed by using a system of 2D partial differential equations to describe the heat and mass transfer effects in addition to the basic polymerization reactions. The second model used 1D coupled nonlinear ordinary differential equations describing the change in the concentration of various polymeric species in the reaction volume. The new third model is based on the stochastic Monte Carlo approach in order to account for the inherently random and discrete nature of the photopolymerization reactions. The simulations of the results obtained from the experiments conducted compared with all models.