One of the reserves for improving the quality indicators of haulm harvesters is to improve the technological process of haulm cutting by improving the design of cutters for haulm residues from the heads of root crops. In this regard, the development of new and improved working bodies for trimming the remains of tops from the heads of chicory root crops and studying the influence of the constructive and kinematic parameters of the cutter in order to improve the performance of haulm harvesters is an urgent scientific task. The developed mathematical models of the process of contact interaction of the copier with the head of the chicory root crop are the initial prerequisites for further technological analysis of cutting the remains of tops from the heads of root crops. The final solutions of integral equations will make it possible to justify the main parameters of the pruner based on the conditions of permissible horizontal force and permissible normal stresses, or from the condition of not knocking out root crops from the soil and not damaging root crops.