The paper reports the working problems and their consequences for composite materials drilling, milling and turning. A bench for computer diagnostics of cutting process at composite materials drilling is developed. The dependences researches in cutting physical parameters influence upon different cutting modes on the basis of the analysis of scientists’ papers and recommendations and also maximum possibility of equipment and mathematical planning of an experiment are carried out. The procedure of two-factor mathematical planning of an experiment is presented. The diagrams of dependences and description of conclusions and recommendations on the application of the bench for computer diagnostics of a cutting process for the choice of optimum cutting modes at the machining of VCU-39 composite material are obtained.