A three-dimensional one-way bubble tracking method is one of the most promising numerical methods for the prediction of a developing bubble flow in a vertical pipe, provided that several constitutive models are prepared. In this study, a bubble shape, an equation of bubble motion, a liquid velocity profile, a pressure field, turbulent fluctuation and bubble coalescence are modeled based on available knowledge on bubble dynamics. Bubble shapes are classified into four types in terms of bubble equivalent diameter. A wake velocity model is introduced to simulate approaching process among bubbles due to wake entrainment. Bubble coalescence is treated as a stochastic phenomenon with the aid of coalescence probabilities that depend on the sizes of two interacting bubbles. The proposed method can predict time-spatial evolution of flow pattern in a developing bubble-slug flow.