Two-phase flow is studied numerically in two dimensions using a two-fluid equation system. The development is based on the surface-tension force terms incorporated in the momentum equations. The governing equations become hyperbolic type for which an upwind method such as flux vector splitting (FVS) avails. As a benchmark problem, a two phase shock tube is first used to study the wave propagation characteristics and interaction between the gas and liquid phases. Fluid sedimentation due to the density difference and cavity growth in a duct with a bend are showed next. Advantages and capabilities of the present formulation are discussed in some detail.