To improve the slab quality, it is essential to design an innovative model for understanding the bubbles' behavior in the continuous casting mold. However, the influence of interaction of bubbles on the motion of dispersed phases has not been considered in most of mathematical simulation models. The purpose of the current work was to establish a new model to simulate the motion of gas bubbles in the mold. In this paper, the mathematical model being related to the interaction of bubbles (coalescence, bounce and breakup) was established using the user-defined functions to predict the behavior and distribution of gas bubbles. Introducing the interaction of bubbles, the size of bubbles will change in the process of collision and broken, so the results can give a good explanation to the motion of different size bubbles, and the phenomena of bubbles coalescence, bounce and breakup actually exist. The results show that the larger bubbles float up to the top surface as soon as they get out of the ports, while the smaller bubbles following the flow arrive at the narrow surface. The proposed mathematical model can described the behavior of bubbles exactly in the steel continuous casting process. (C) 2014 Elsevier B.V. All rights reserved.