This paper presents a new and accurate methodology for transient and dynamic behavior of slug hydrodynamic instability modeling in horizontal and inclined channels. The base of this methodology is on numerical solution of hyperbolic two fluid model equations by means of a class of high resolution shock capturing methods. The privilege of this method is that it can model and predict initiation and growth of slug in stratified flow automatically and directly by solving the flow field differential equations. The well-defined test case considered for the verification and validation of the results is the Ransom Water Faucet case. The results obtained for slug flow modeling in horizontal duct were compared with two sets of experimental results. The good agreement of the present modeling results with the experimental results of own and other investigators and also grid independency study show the model is capable of slug tracking and slug capturing and the numerical method which is used here can predict with high enough accuracy.