In the gas and oil offshore deep water production is usual to find risers in Production Unit final approach. Regarding to this configuration, two-phase flows can evolve to a severe slug regime that create gas and liquid alternate production. This cyclic behavior is characterized by periods of gas production followed by very high liquid and gas flow rates. The severe slug flow regime is normally described as occurring in four phases: slug formation, slug production, blowout, and liquid fallback. This flow regime introduces new conditions that can be found in other regimes because of the pressure increase during the slug formation and the large flow rates during the slug production. The present work consists of the numerical simulation of the severe slug flow regime into a horizontal pipeline section followed by a vertical section, as well as to present an statistically steady state analysis. The flow prediction is obtained through a one-dimensional formulation based on the Drift Flux Model. The slug frequency is compared with other numerical studies available in the literature, and a very satisfactory agreement is obtained.