In one of the last stages of paper production the surface of the paper is refined in calenders. The paper is compressed in the nip by rollers which sometimes tend to exhibit self-excited vibrations. These vibrations may lead to wear and dramatically reduce the durability of the expensive rollers. The reason for the self-excited vibrations is to be found in the interaction of the rollers with the paper. The interaction process in the nip is very complex and has not been completely understood from a mechanical point of view. The purpose of this paper is to develop simple mechanical models of the nip which can lead to an explanation of the phenomenon.