The microstructure and hardness profiles across a friction stir welded joint of a 2024-T3 aluminium alloy have been simulated by thermal and microstructure models. Thermal modelling is based on a semi-analytical model, which analyses the complex material flow by standard velocity fields. The precipitation model is based on classical nucleation, growth and coarsening mechanisms and can be combined with precipitation hardening laws. Applying these models in succession gives simulated hardness profiles, which have been compared to experimental hardness values after friction stir welding under equivalent conditions. The positions of maximum and minimum hardness are well reproduced, but the simulated hardness variation across the weld is less pronounced than the experimental one. The simulated microstructures in well characterised zones of the joint have been compared to previous TEM observations and shown to be generally in agreement. The results demonstrate the feasibility of making realistic hardness predictions from physically based models on a standard personal computer.