Aluminium alloy sheets cause many problems in sheet metal forming processes owing to their tendency to gall the surface of the tool. The paper presents a method for the determination of the kinematic friction coefficient of friction pairs. The determination of coefficient of friction (COF) in sheet metal forming requires specialised devices that ‘simulate’ friction conditions in specific areas of the formed sheet. In this article, the friction behaviour of aluminium alloy sheets was determined using the strip drawing test. The 1-mm-thick 6082 aluminium alloy sheets in T6 temper were used as test material. Different values for nominal pressures (4.38, 6.53, 8.13, 9.47, 10.63, and 11.69 MPa) and different sliding speeds (10 and 20 mm/min.) were considered. The change of friction conditions was also realised with several typical oils (hydraulic oil LHL 32, machine oil LAN 46 and engine oil SAE 5W-40 C3) commonly used in sheet metal forming operations. Friction tests were conducted at room temperature (24 °C). The main tribological mechanisms accompanying friction (adhesion, flattening, ploughing) were identified using a scanning electron microscope (SEM). The influence of the parameters of the friction process on the value of the COF was determined using artificial neural networks. The lowest value of the COF was recorded when lubricating the sheet metal surface with SAE 5W40 C3 engine oil, which is characterised as the most viscous of all tested lubricants. In dry friction conditions, a decreasing trend of the COF with increasing contact pressure was observed. In the whole range of applied contact pressures (4.38–11.69 MPa), the value of the COF during lubrication with SAE 5W40 C3 engine oil was between 0.14 and 0.17 for a sliding speed of 10 mm/min and between 0.13 and 0.16 for a sliding speed of 20 mm/min. The value of the COF during dry friction was between 0.23 and 0.28 for a sliding speed of 10 mm/min and between 0.22 and 0.26 for a sliding speed of 20 mm/min. SEM micrographs revealed that the main friction mechanism of 6082-T6 aluminium alloys sheet in contact with cold-work tool steel flattens surface asperities. The sensitivity analysis of the input parameters on the value of COF revealed that oil viscosity has the greatest impact on the value of the COF, followed by contact pressure and sliding speed.