[en] The method of characteristics is an exact way to proceed to the solution of hyperbolic partial differential equations. The numerical solutions, however, are obtained in the fixed computational grid where interpolations of values between the mesh points cause numerical errors. The Piecewise Linear Interpolation Method, PLIM, the utilization of which is based on the method of characteristics, has been developed to overcome these deficiencies. The thesis concentrates on the computer simulation of the two-phase flow. The main topics studied are: (1) the PLIM method has been applied to study the validity of the numerical scheme through solving various flow problems to achieve knowledge for the further development of the method, (2) the mathematical and physical validity and applicability of the two-phase flow equations based on the SFAV (Separation of the two-phase Flow According to Velocities) approach has been studied, and (3) The SFAV approach has been further developed for particular cases such as stratified horizontal two-phase flow. (63 refs., 4 figs.)