The influence of various process parameters on the deep drawing process is a current research topic in sheet metal forming technology. Starting from the application of the previously constructed original testing device, an original tribological model was developed based on the process of sheet metal strip sliding between flat contact surfaces under variable pressures. A complex experiment was executed using an Al alloy sheet, tool contact surfaces of different roughness, two types of lubricants and variable contact pressures. The procedure included analytically pre-defined contact pressure functions based on which, for each of the mentioned conditions, the dependencies of the drawing forces and friction coefficients were obtained. The pressure in function P1 constantly decreased from a high initial value until the minimum, while in function P3 the pressure increased until the minimum value at the halfway point of the stroke, after which it increased up to the initial value. On the other hand, the pressure in function P2 constantly increased from the initial minimum value until the maximum value, while in function P4 the pressure increased until reaching the maximum value at the halfway point of the stroke, after which it decreased to the minimum value. This enabled the determination of the influence of tribological factors on the process parameters of intensity of traction (deformation force) and coefficient of friction. The pressure functions starting with decreasing trends produced higher values for the traction forces and the friction coefficient. In addition, it was established that the roughness of the contact surfaces of the tool, especially those with titanium nitride coating, has a significant influence on the process parameters. For surfaces of lower roughness (polished), a tendency of the Al thin sheet to form a glued-on layer was noticed. This was especially prominent for lubrication with MoS2-based grease under conditions of high contact pressure (functions P1 and P4 at the beginning of the contact).