In the article, a new, developed by the authors mathematical model of the process of plant material cutting with use of a shear - finger cutting section, has been presented. Innovatory nature of this model involves a new approach to the plant material to be cut. Other, so far developed models do not take into account the stalk stiffness changes along its length, which in the opinion of the authors is a too big simplification. The computer program named ŹDŹBŁO 1 was performed for needs of the simulation analysis. This program can be applied at the stage of design of the shear-finger cutting section. It should be observed that these mechanisms are widely used in agricultural machines.machines.