The subject of the study is methods for determining vessel volume with complex shapes. The aim of the study is a development and scientifically substantiate of a method for fast measurement of an internal cavity volume of a vessel having a complex geometric shape in a gaseous medium based on supercritical outflow. The task of the study is the development of a method for calculating the volumes of the gas path components for the previously proposed generator of gas mixtures, which based on the supercritical outflow from intermediate tanks with constant volume, and confirmation of the proposed method capabilities using a simulation of the volume measurement process by the same method. The following results were obtained. It is proposed the method for fast measurement of vessel volume with complex shape based on supercritical flow through nozzles with the predetermined flow rate and dynamic measured pressure. The range of measurement time is substantiated for which, on the one hand, the conditions for suppressing transient processes in the measured vessels after the beginning of the supercritical outflow of the process gas are satisfied, and on the other hand, the conditions for adiabatic outflow are provided. According to the simulation of measuring the volume of a complex-shaped vessel using the proposed method, the accuracy of determining the volume of the vessel was 0.0625% in relation to the CAD system data. To use the proposed method in practice, the measuring equipment should include a reference vessel, and the measurements themselves should be carried out in two stages, using the same gas for filling in both cases. In this case, at the first stage, according to the results of the control measurement when it expires from the reference vessel, the value of the flow coefficient is specified, and at the second stage, when it expires from the measured vessel, the required target volume is determined. The process of direct volume measurement, in this case, lasts up to 1 second, the accuracy of volume determination is expected to be 0.1%.