[en] An accurate prediction of transient two-phase flow phenomena is quite important in safety analyses of nuclear reactors under normal, off-normal or accident conditions. In general, the ability to predict these thermohydraulic phenomena of two-phase flow depends on the availability of mathematical models and experimental correlations. The fluid flow and heat transfer encountered in reactor safety analyses are often very complex due to reactor geometries. Furthermore, full scale experiments with sufficient instrumentations are often extremely difficult to perform due to its size and adverse conditions. These indicate the importance of accurate two-phase flow models and constitutive relations which take into account the widely varying properties, system scales and geometrical effects. The algorithm used in this paper is Newton Block Gauss Seidel (NBGS) method, which has been applied to both simple and complex flow conditions in two-phase flow. This paper contains a description of difference techniques and iterative solution algorithm that is used to solve the field and constitutive equations of the two-fluid model. In practice this solution procedure has been proven to be stable and capable of generating solutions in problems where other schemes have failed. Examples of transient two dimensional air-water flow with in channels and bends with variation of inlet slip ratio and void fraction is being presented in this paper