A number of accurate constitutive equations are required for reliable prediction of multidimensional two-phase flow. However, few constitutive equations have been established due to the lack of (1) simple numerical methods for solving governing equations of multidimensional two-phase flow and (2) reliable experimental data on multidimensional two-phase flow. In the present study, a simple and efficient numerical method for solving a multidimensional incompressible two-fluid model, which is based on the simplified marker and cell (SMAC) method, was proposed to facilitate the development of constitutive equations. This method enables us to calculate multidimensional two-phase transient phenomena with a personal computer. Details of the present method and a comparison of measured and predicted two-dimensional flow patterns of two-dimensional bubbly flow are described.