Abstract: When severe slugging is formed, the parameters of air-water riser systems (e.g. pressure and internal transient flow rate) will fluctuate in a large range. As a result, the downstream equipments are impacted and pipelines tend to suffer violent vibration. In order to evaluate the hazard of severe slugging, it is necessary to calculate its transient flow parameters accurately. In this paper, a transient mathematical model for severe slugging was developed on the basis of the continuity equation for liquid and gas and the momentum equation for the mixture. Then, the numerical integration method was illustrated in detail. And finally, the severe slugging in a riser testing unit was simulated numerically, and the simulation results were verified. The numerical integration was predicted by the backward Euler scheme and corrected by means of trapezoidal method. Variable time step was employed to improve computational efficiency and accuracy. Laboratory experiments were performed on severe slugging, and the experimental results were compared with the simulation results in terms of cycle periods and bottom pressure. The simulation results of transient flow parameters (e.g. gas flowing velocity, liquid flowing velocity and void fraction) were compared with the calculated results of Fluent. It is indicated that this mathematical model and numerical method can calculate the transient flow parameters of typical severe slugging in a better way, and they play an important role in evaluating the hazard of severe slugging accurately.