This paper presents a new and accurate method for modeling dynamic and transient behaviors of slug initiation and growth in horizontal ducts. In this analysis, a hyperbolic, two-pressure, five-equation, two-fluid model predicted the dynamic behavior of a complicated slug flow regime. The model was modified by including friction with the wall and at the interfaces between phases. In this paper, highly accurate shock capturing numerical methods were applied to slug modeling for the first time. The applied method is low cost, simple and does not exhibit the problems of previous numerical methods, such as the high computational time associated with the finite volume of two-fluid models. The new method does not use experimental correlations and assumptions to simplify the model like unit cell and slug tracking methods. In the present work, the numerical method of AUSMDV was used for a one-dimensional, two-pressure, five-equation, hyperbolic, two-fluid model. The calculation is conducted by applying second order time and space accuracy. The AUSMDV numerical method does not identify a complicated matrix solution; therefore, it renders the flow field solution using minimal computational resources. Discretization of non-conservative products that appear in the momentum equations was performed using a conservative linear path scheme (based on path conservative schemes by Pares), and accurate discretization of non-conservative terms based on AUSM fluxes have been conducted. Numerical solutions are presented for well-defined problems of two-phase, gas–liquid flows. The well-defined test cases that were considered for verification and validation are the Reiman Shock Tube and the Ransom Water Faucet. Numerical estimates of slug flows in horizontal ducts were compared with two sets of experimental results. Good agreement between modeled and experimental results, as well as a grid independency study, suggests that the presented model is capable of slug tracking and slug capturing. In addition, the numerical method that is used here can predict flows with sufficient accuracy. Finally, several facts related to the physics of slug behavior were outlined. These facts could be useful for scientists who wish to model the flow regime correctly, and they may be important for system designers who must predict slug behavior physically.