The behaviour of square hollow section AA6060 aluminium profiles subjected to quasi-static axial crushing was investigated experimentally and numerically. The profiles were artificially aged to three different tempers (under-aged, peak-aged and over-aged) using two different cooling rates (water quench or air cooling) after the solution treatment, thus obtaining six different materials. The materials’ microstructures were characterized by scanning and transmission electron microscopy and mechanical testing was used to determine the stress–strain curves in uniaxial tension. Axial crushing tests were carried out on profiles made of the six different materials to study the influence of the heat treatment on the energy-absorbing capability of the profile. The nanometre-scale material model NaMo was employed to predict the stress–strain curves of the three water-quenched materials based on the chemical composition and the thermal history. A new feature was introduced in NaMo in order to account for the incubation period, which cannot be ignored for low-alloy materials such as the AA6060 alloy. The stress–strain curves predicted using the improved nano-scale material model showed good agreement with the experimental curves for the three tempers when the incubation period was considered. Using the predicted stress–strain curves in finite element simulations of axial crushing of the profiles, gave excellent predictions of the experimentally obtained force–deformation curves and thus the energy absorption. The results indicate that two-scale simulation based only on chemical composition and thermal history is now possible in designing AA6xxx structural components for safety applications.