A high-resolution upwind scheme based on the flux vector splitting method is developed for the two-fluid six-equation model to solve the wave propagation problems of the two-phase flow. The interfacial pressure jump terms make the governing equations hyperbolic without any conventional source terms in the momentum equations. Real eigenvalues are obtained for all the bubbly, slug, and annular flow regimes. Calculated speeds of sound have shown excellent agreement with the existing experimental data. Solutions to wave propagation problems with initial pressure and void distribution are presented. The Edwards pipe problem accompanied by sudden depressurization and flashing also is solved as a benchmark test.