Since the middle of the 20th century several studies concentrate on the mathematical description of the cutting process of wood. In order to resolve this problem, empirical as well as analytical approaches were applied. Despite extensive research until now still no practical as well as a complete description of the interaction process of wood cutting exists. For this reason the aim of the following work is bringing together different approaches to develop an accurate and yet user-friendly explanation of cutting forces in wood, likewise in the metal working industry. Basic requirement is the consistent use of the general definitions. Therefore this part of the work deals with the geometric principals of the cutting process. Furthermore previously developed models, especially empirical models, are presented. Additionally assets and drawbacks of the analytical models are discussed.