The modern scientific and technological revolution has led to profound changes in the technique and technology of marine seismic research, ensuring an increase in labor productivity, a significant increase in the volume of work, as well as an increase in their efficiency. At the same time, along with the use of floating piezoelectric seismograph, digital recording equipment, modern electronic computing equipment and more accurate satellite navigation systems, one of the important factors that contributed to improving the efficiency of seismic exploration was the introduction of a new generation of seismic signal excitation devices – non-explosive sources – into the practice of marine seismic research. Of these, the most widely used in seismic exploration in water areas around the world are pneumatic sources, in which elastic waves are excited by underwater exhaust of compressed air. The purpose of this work is to select and justify a theoretical model that adequately describes the process of pulsation in the water of the air cavity, as well as its acoustic radiation. The model chosen as a result can be used for mathematical modeling of new designs of pneumatic sources that are being developed.