<p>This paper presents both experimental and numerical results of the orthogonal cutting process of aluminium alloy EN AW 6082 T6. A Coupled Eulerian–Lagrangian formulation was applied in a thermal–mechanical numerical model of orthogonal cutting. In order to develop a numerical model that predicts output values with sufficient accuracy compared to the experimental results, it was necessary to apply the exact hardening law and accurately describe the contact conditions between the tool and workpiece. Different numerical models and hardening laws were compared in terms of predicting cutting forces and temperature in the cutting zone. Two expressions for the hardening law have been proposed based on the Johnson–Cook hardening law and the Arrhenius hardening law. In the first proposed law, the influence of temperature is additionally described by a logarithmic function, while the second law contains a hyperbolic tangent function. Subprograms (VUHARD) have been developed for the specified hardening laws. The accuracy of the numerical models was tested for a wide range of feeds and cutting speeds by comparing numerical predictions with experimental results. All the analysed hardening laws result in the same predictions: cutting forces increase with increasing feed, decrease with increasing cutting speed and the temperature in the cutting zone increases significantly as cutting speed increases. However, there is a significant difference in the prediction of the output parameter values when different hardening laws are applied.</p>