The purpose of this article is to better understand the behavior of the residual stresses in aluminium alloy plates by using mathematical modelling. Quenching of aluminium alloy plates causes an uneven temperature variation in aluminum alloy plates, and elastic and elasto-plastic deformations occur inside the material. The latter causing the formation of deformations and residual stresses. The non-linear thermo-mechanical direct coupled analysis of the quenching process for a 6061 aluminium alloy plate was achieved by using ANSYS finite element software. The residual stresses due to solid thermal effects were determined by calculation of the Third principal stresses, the most negative or compressive. The developed mathematical model offers a support in the understanding the behavior of the residual stresses in aluminium alloy plates and a better control of them.