Results on 3-dimensional mathematic simulation of processes in flow parts of hybrid turbomolecular pumps (TMP) are presented. Description of algorithms and of a calculation programs complex for characteristics of hybrid turbomolecular pumps with molecular and drum forcing channels is given. The influence of geometric parameters of a flow part on an operation rate and a maximal compression degree of pump channels is investigated. The concept of optimisation of hybrid pumps under restrictions of controlled parameters is developed.The optimal variants of a flow part are given. Rated and experimental data are compared. There is developed an algorithm of optimization of a TMP flow part with axial and axial-radial gas flow under functional restrictions on controlled parameters, ensuring the desired TMP operation rate at fixed suction pressure for a chosen gas, and also the desired operation rate for several gases using the algorithm of slipping access and the absolute penalty functions metod. It is found out, that within the investigated operation rate's range an axial-radial scheme has better mass-size characteristics compared to that of an axial scheme. Decrease in volume of a flow part with optimal geometric parameters makes from 36 % (S=0.5 m@super3@/sec) to 53 % (S=20 m@super3@/sec) due to decreasing the axial rotors number. Here the external diameter of axial rotors increased from 35 % (S=0.5m@super3@/sec) to 5 % (S=20m@super3@/sec). More preferable is the axial-radial scheme with periphery-center flow direction. It is found out, that if ensuring the desired raised evacuation characteristic for light gases, the flow part volume of all the three schemes increases due to increase in axial rotors number and smoother changing of geometric parameters over rotors, and mass-size characterictics of axial-radial schemes come worse. Decrease in the flow part volume comparing to that of an axial scheme makes for the scheme with periphery-center flow 24 % (S=20m@super3@/sec, P=10@super-5@ Pa, S=15 m@super3@/sec and P=10@super-3@ Pa). The volume of an axial scheme raised on 93 %, of axial-radial schemes - on 163 % and 150 % compared to the computation results when ensuring the desired operation rate only for nitrogen.