The advantages of application on production of radial flow gripping devices of industrial robots are justified. The mathematical model for numerical modeling of dynamics of air flow in nozzle of radial flow gripping devices and in radial interval between its active surface and surface of object of manipulation is presented. For this purpose it is used averaging on Reynolds of Navier-Stokes’s equation of dynamics of viscous gas, SST model of turbulence and γ-model of laminar and turbulent transition. Technical requirements to design of radial flow grippers are defined and options of their constructive improvement are offered. The formula for calculation of the minimum diameter of nozzle of radial flow gripper is offered. By the results of numerical modeling in the program Ansys-CFX environment influence of geometrical parameters of nozzle and active surface of radial flow gripping devices on the nature of distribution of pressure in radial interval and its upward force is defined.