Kinetic gelation models simulate free-radical polymerization on fixed lattices, where propagation and termination reactions are restricted to occur only between nearest neighbors. Here such a model is used with bifunctional sites and with kinetics recast as a Markov process through a stochastic approach. The reaction time is calculated by employing the probability density function and associated Monte Carlo method devised originally by Gillespie. As polymerization proceeds, the evolution of structure is characterized by pair correlation functions of three types-of reacted sites, of doubly reacted sites, and of monomers. These show that as polymerization proceeds, reacted sites and doubly reacted sites come to be distributed more uniformly in space; monomers come to be distributed less uniformly. A higher initiation rate constant, a higher initiator concentration, and a lower propagation rate constant lead to more uniform distribution of reacted sites, of doubly reacted sites, and of monomers. These factors also lead to lower average connectivity between reacted sites. These trends are strongest at low conversions. In contrast, an enhanced primary cyclization leads to less uniform distribution of reacted sites but to more uniform distribution of monomers. It also leads to higher connectivity between reacted sites that are close together but to lower connectivity between reacted sites that are far apart. Finally, at high conversions it leads to a more uniform distribution of doubly reacted sites.