In this paper, by using theory of contact mechanics, there has been developed a new calculation model for calculation of coefficient of friction, which based not only to mechanical, but also to the adhesion forces, which occurs between contacting surfaces in friction pair. Adhesion forces influences coefficient of friction and this influence can be seen in following result diagrams. By further calculations, there were discovered proof to specific friction behavior on smooth surfaces, which means that if for smoother surfaces mechanical component of coefficient of friction is getting smaller, but adhesion component is getting larger. It can be explained by fact that for smooth surfaces, especially for those surfaces where roughness can be found only at nanoscale level, there is smaller distance between both surfaces, which leads to greater influence from Van der Waals interactions.