Wave propagation in the two-phase flows has been numerically investigated. The waves have been generated by various means such as two-phase shock tube, pressure pulse, and void pulse wave. The six compressible two-fluid conservation laws with the interfacial friction terms are solved in the two fractional steps. The first PDE operator step makes use of analytic eigenvalues of an approximate Jacobian matrix in HLL scheme. The second source operator step makes use of the stiff ODE solver in a semi-implicit form. The waves in the two-phase flow field resolved by the present method have shown very small numerical diffusion. An assessment is made on the effect of interfacial friction terms included in the formulation.