Friction is one of the fundamental factors describing the functioning of mechanical systems, which is why it has been the subject of extensive scientific research for years. Despite the undoubted progress in research, modeling friction processes is still an attractive scientific challenge. The article presents a method of modeling friction (kinetic and static, including the so-called "stick-slip") occurring in discrete mechanical systems. A characteristic feature of the method is the use of special luz(...) and tar(...) projections together with their original mathematical apparatus, thanks to which the friction process models are transparent, allow for parametric reduction and adapted to standard numerical procedures used in simulation. The author's method through its application in the synthesis of an unpublished stick-slip model for a three-element system with two friction pairs. The determined model can be useful in modeling layered structures. It should be noted that analyses of stick-slip processes in layered structures can occur in the problems of soil and building mechanics.