Classical Molecular Dynamics (MD) simulations provide insight into the properties of many soft-matter systems. In some situations, it is interesting to model the creation of chemical bonds, a process that is not part of the MD framework. In this context, we propose a parallel algorithm for step- and chain-growth polymerization that is based on a generic reaction scheme, works at a given intrinsic rate and produces continuous trajectories. We present an implementation in the ESPResSo++ simulation software and compare it with the corresponding feature in LAMMPS. For chain growth, our results are compared to the existing simulation literature. For step growth, a rate equation is proposed for the evolution of the crosslinker population that compares well to the simulations for low crosslinker functionality or for short times.