A semi-empirical model is proposed to represent the scavenging process in cross, loop or uniflow scavenged engines. The model is based on the assumption that in most cases (if not in all) the time variation of the mass fraction of fresh air content in the gas passing through the exhaust port (β) exhibits an “S” type curve. An exponential function of the form of is suggested to fit this curve where the shape and the form factors may consider any combination of perfect displacement, perfect mixing and short-circuiting processes. The charging efficiency was then calculated and compared with other models - the isothermal mixing, the non-isothermal mixing, the Benson model and a detailed computer model. The new model has been found as a realistic model for modern engine design and an easy-to-use model for computer simulations.