A precipitate evolution model based on classical nucleation, growth and coarsening theory is adapted and solved using the multi-class approach for the superalloy IN718. The model accounts for dissolution of precipitates and is implemented in a finite element program. The model is used to simulate precipitate evolution in the fused zone and the adjacent heat affected zone for a welding simulation. The calculated size distribution of precipitates is used to predict Vickers hardness. The simulation model is compared with nanoindentation experiments. The agreement between simulated and measured hardness is good.