Transient two-phase flow in pipes is a common phenomenon in nuclear and petroleum engineering. Due to complex interactions at phase interfaces and the large variation on fluid properties, multiphase flows are much more complex than single-phase flows. However, modeling pressure, temperature, phase velocities and volumetric fractions is essential for design, management, optimization and safety analysis. Two approaches are generally applied for modeling multiphase flow: (a) local instant formulation and (b) averaged formulation. In this paper, the averaged Single-Pressure Two-Fluid model (together with Bestion’s correlation for interfacial pressure) is studied and a fully-implicit numerical solution is proposed. The obtained numerical solutions were compared to reference solutions for benchmark problems (water faucet tests and phase segregation) available in the literature. Aiming to verify if the aforementioned averaged model and the proposed fully-implicit solutions can be applied to study problems with counter-current flow and sharp discontinuities in pressure, velocities and volumetric fractions, new reference solutions for a generalized transient frictionless segregation test are proposed. Comparison between the proposed reference and numerical solutions allowed for a detailed verification of the studied averaged model. Finally, sudden multiphase fluid injection with subsequent tube closure was studied and the numerical results were discussed. As expected, it was observed transient surge pressure and co-current/counter-current flow with phase appearance and disappearance.