This paper presents a three-dimensional model of an airbag located outside of a small city car at the front bumper, which is intended to protect the vehicle against the effects of road traffic collisions. Results of numerical simulations of airbag operation in case of collision with two types of obstacles are presented: a flat, vertical wall and a circular pillar with a diameter of 200 mm. The paper presents the physical model, which is the subject of simulation, along with its mathematical description and the numerical calculation scheme used.