Modeling free radical polymerization processes in the presence of cross-linkers is a challenging problem that has been addressed using numerous techniques for over more than half a century. However, a model providing a comprehensive description of the phenomenon has not been proposed yet. In this work, we implement a simple free-radical polymerization scheme of a monovinyl (difunctional) monomer and a divinyl (tetrafunctional) cross-linker in a Monte Carlo (MC) scheme, which describes polymer dynamics using a bond-fluctuation model. MC simulations allow us to follow the entire polymerization kinetics and the formation of a percolating network (gel phase) by realistically taking into account diffusion limitations, to extract scaling information at the percolation threshold and to recover the distribution of number of monomer units between two successive fully cross-linked units, from which the extent of swelling can be computed. The predictions of MC simulations are also successfully compared to a kinetic model based on numerical fractionation, with kinetic constants used as fitting parameters. MC data and kinetic simulations are compared to some experimental data on the swelling behavior of polyacrylamide hydrogels and of poly(methyl methacrylate) (PMMA) gels, exhibiting good agreement. We conclude that the proposed MC simulation scheme represents a powerful tool from which precious and experimentally inaccessible information on polymerization processes in the presence of cross-linkers can be extracted.