The article is focused on dynamic modeling and simulation of pulmonary compartment behaving and response during gas flowing in the lungs. Dynamical simulations based on the differential equations represent time-depended models describing dynamic state of individual gases in the lungs and other tissues. The pulmonary system model includes the two ways: derivation of mathematical model for individual parts respiratory system, and numerical simulation of these parts. Dynamical model behavior is based on the set of differential equations allowing for dynamical description of entire pulmonary compartment. These simulations are especially important for understanding pulmonary system during gas cycle, and also serve for prediction of behaving pulmonary diseases.