This paper presents an analytical treatment of a mechanical-mathematical model of an air bag inflation process integrated with a model for the interaction between the air bag and a standing child dummy. The inflation model consists of a one-dimensional gas dynamics analysis of the flow system which delivers the gas to inflate the bag. The interaction model then provides a method for calculating the forces exerted by the inflating bag on the standing child. The results show that the unacceptably high contact forces recorded in standing-child air bag tests are due to impact of the unopened portion of the bag on the standing child. A single-membrane concept is thus suggested to reduce this impact severity.