The processing accuracy and productivity of metal-cutting machines are largely determined by the initial characteristics of the spindle assembly, since it is the last link in the kinematic chain of the main drive. Therefore, high demands are placed on spindle assemblies to ensure high rotational accuracy, high speed, parametric reliability, etc. Since the movement of shaping is carried out by the spindle and spindle bearings, they make a decisive contribution to the initial characteristics of the spindle units. The installation of spindles on gas bearings makes it possible to significantly increase the accuracy of rotation and speed of the spindle, almost completely eliminate its vibration, simplify the design and significantly increase the parametric reliability of the spindle assembly. The parameters of the gas lubricating layer in the conical bearings of the spindle are investigated and the equation of gas pressure in the gaps of the gas conical bearing with grooves of different profiles applied to the bearing shaft of the spindle is derived. The optimal geometric parameters of the profile of longitudinal blind grooves applied to the working surfaces of the spindle shaft are determined. Investigations were carried out using numerical methods using modern software.