The Pressurized Water Reactor vessel steels are embrittled by neutron irradiation. Among the solute atoms, copper play an important role in the embrittlement and different Cu-rich defects have been experimentally observed to form. We have investigated by Kinetic Monte Carlo (KMC) on rigid lattices the evolution of the primary damage. Since the point defects created by the displacement cascades have very different kinetics, their evolution is tracked in two steps. In a first step, we have studied their recombination in the cascade region and the formation of interstitial clusters using “object diffusion”. The parameters of this model are based on MD simulations, or on first principles calculations. In a second part, we have investigated the subsequent evolution of the primary damage with a model based on a vacancy jump mechanism. These simulations which rely on an adapted EAM potential show the formation of copper rich defects. Some of the potential's predictions that played a key role in the model were checked by ab initio calculations. The defects obtained from these simulations, subsequent to the primary damage created by displacement cascades, exhibit similarities with the ones observed by atom probe. The influence of temperature and Cu content on the final damage was investigated.