Flux vector splitting method is applied to the two-fluid six-equation model of two-phase flow, which takes account of surface tension effect via the interfacial pressure jump terms in the momentum equations. The latter terms using the concept of finite-thickness interface are derived as a simple function of fluid bulk moduli. We proved that the governing equation system is hyperbolic with real eigenvalues in the bubbly. slug, and annular flow regimes. The governing equations do not need any conventional artificial stabilizing terms like the virtual mass terms. Sonic speeds obtained through characteristic analysis show excellent agreement with the existing experimental data. Edwards pipe problem is solved as a benchmark test of the present two-phase equation model. (C) 2002 Elsevier Science Ltd. All rights reserved.