Relevance. It is known that in response to the onset of physical exercise, lung ventilation increases very quickly, within a few seconds. Existing theories of breathing control based on the blood gas composition cannot explain the rapid ventilation increase solely due to an increase in the tissues’ oxygen consumption and carbon dioxide production. Cardiodynamic hyperpnea and muscle pump with peripheral vasodilation mechanisms suggest that systemic and pulmonary blood flow increases rapidly at the physical exercise onset. At the same time, the ventilation to blood flow ratio immediately decreases. Therefore, the CO2 content increases and O2 content decreases in the arterial blood flowing from the lungs. When this blood reaches the peripheral sinocarotidsinus chemoreceptors, the increased impulses from the chemoreceptors cause a rapid increase in the lung ventilation. Although these physiological mechanisms require thorough experimental clarification, mathematical simulation allows us to investigate which certain mechanisms can explain the experimental data on the rapid response of the cardiorespiratory system to the physical exercise onset. The aim of this study is to develop a human breathing regulation and pulmonary gas exchange mathematical model, applicable for the human gas exchange and ventilatory response to moderate physical exercise simulation over periods of about 7 minutes. Model verification by the qualitative comparison of the simulation results with literature data confirmed its adequacy. Results. A compartment mathematical model with four reservoirs (pulmonary, tissue, cerebral, and external) has been created. The model includes the equations of: gas exchange, Ben-Tal lung mechanics, chemoreflective regulation of Magosso-Ursino and blood transport properties. The verification was carried out by comparison with experimental data. Conclusions. At a qualitative level, the theory of “cardiodynamic hyperpnea” describes well the cardiorespiratory system’s response to physical exercise. The blood flow & ventilation rapid increase in response to physical exercise onset and subsequent slower processes in the respiratory response to physical exercise are manifested in the alveolar fractional concentration of CO2 increase, in the alveolar fractional concentration of O2 moderate decrease and in a following ventilation additional increase, expressed by the interaction of peripheral and central chemoreflexes.