The entrapped air pockets in a pressurized water supply pipe may produce a significant transient pressure, resulting in pipe deformation or even pipe rupture. This article focuses on the maximum pressure of entrapped air pockets in a rapid filling pipe and its influencing factors. In this paper, the rigid water column theory and the ideal gas equation are applied to the air vessel-pressured pipe–air pocket system, and the theoretical formula representing the relationship between the maximum air pressure (MAP) and air comprehensive coefficient is presented. In addition, a numerical model of the system is established by the method of characteristics. The rapid filling process is simulated according to the experimental setup and the results are in good agreement with the experimental data. The influence of the air comprehensive coefficient on the MAP is also studied. Both the theoretical formula and numerical simulation show that the smaller air comprehensive coefficient will result in larger MAP (i.e., the MAP decreases with the increase of the polytropic exponent and initial air pressure, and increases with the increase of the initial air length).