In this manuscript, we discuss the implementation of an upwind method for a new two-dimensional two-fluid model by including the surface tension effect in the momentum equations. This model consists of a complete set of eight equations including two mass, four momentum, and two internal energy conservation equations, all with real eigenvalues. Based on this equation system, we first made a characteristic analysis for investigating mathematical properties. Next, we made a two-dimensional pilot code based on the HLL scheme to solve some benchmark problems in order to determine whether this model and numerical method can simulate a fundamental two-dimensional two-phase flow problem as well as one-dimensional problems. (C) 2012 Elsevier Inc. All rights reserved.