(1) Purpose: The effect of axial movement of piston rings in the piston grooves is estimated by calculation and experimentally for the passage of gases in an internal combustion engine (ICE). (2) Methodology: When modeling the effect of axial movement of piston rings in the piston grooves for the passage of gases in the ICE, theoretical positions are used. It is based on the fundamental theory of heat engines, thermodynamics and hydraulics. Running was investigated using theoretical and theoretical research methods; (3) Results: The effect of axial movement of piston rings in the piston grooves on the passage of gases in the ICE is established. This creates prerequisites for a more accurate assessment of their sealing ability and the search for ways to further improve them. Calculated dependences are obtained for calculating the pass of gases depending on the relative position of the rings in the piston grooves. The dependences of gas escapes on the engine crankshaft rotation speed are obtained, which is especially important for idling modes, by which one can judge the dynamic stability of the ring seal and solve the problems of improving its operational properties; (4) Practical implications: This paper proposes the practical method for estimating the dynamic stability of an annular seal based on gas escape dependencies on the crankshaft rotation speed in ICE is proposed. In addition, this study contributes to the development of practical recommendations for the further improvement of engine ring seal designs.