The analysis of two-phase flow is greatly important for numerous applications in engineering, such as, cooling, nuclear industry and specially, oil industry, wherein oil and gas production carry fluids mainly in liquid and gas phases. Thus, it becomes crucial the study of the behavior of said phases flowing in a pipeline, aiming to give support and to operate pipelines. In this work focus will be given to stratified flow. In the present work, the performance of a methodology for predicting the one-dimensional stratified flow pattern was assessed, using the Two-Fluid Model. An analysis of the liquid and gas phases superficial velocities influence on the interfacial waves amplification rate was performed. The prevision of the interfacial waves amplification rates using 1st (Upwind) and 2nd (TVD) order spatial discretization schemes was investigated. The prediction proficiency in 1st (Implicit Euler) and 2nd (Crank-Nicolson) order temporal discretization schemes was also investigated. The obtained results were compared to linear stability analysis data. For validating the model used, the pressure drop prevision was also compared with experimental data available in the literature.