After the extrusion process most aluminium alloy profiles don´t satisfy the necessary strength requirements. An increase of strength can be obtained by age hardening of hardenable aluminium alloys. Age hardening includes the three steps of solution annealing, quenching and aging and is usually carried out in a separate process after extrusion. The integration of the sub-steps solution annealing and quenching in the extrusion process results in a marked reduction of the complete process chain. The applicability of this integration depends primarily on the quenching power of the cooling module and on the quench sensitivity of the aluminium alloy. Using the finite element method the non-steady-state process of quenching the profiles after leaving the extrusion press has been simulated. The boundary conditions for quenching are varied for a gas nozzle field and a spray cooling using heat transfer coefficients based on experiments. The simulation results support the design of gas nozzle fields or spray cooling for the extrusion process of different aluminium alloys.