New model of the simulation of the airbag inflation process, taking into account the influence of the airbag environment on the folding process, have been proposed. Equations describing a new model and the used numerical schemes were presented. The differences of the airbag fabric skin motion during the folding process, obtained by the use of different process models (existing and proposed), have been presented on the simple geometry examples. From the analysis of obtained results one acknowledged that the proposed model should be used in all calculations of the airbag operation in non-typical situations, out-of position occupants, side airbags, particularly in the case of small distances between the closed airbag and the elements of the body of the protected person.