Heavy oils, due to their high viscosity, have greater viscous resistance to flow, requiring high pumping power for transport and increasing operating cost. As an alternative to minimize this problem, the core-flow technique emerged, which consists of injecting water simultaneously with the oil flow, causing the heavy oil to be surrounded by a layer of water and flowing in the center of the duct without touching the pipe wall, consequently reducing the friction pressure gradient. Thus, this work aims to numerically study the core-annular flow of oil, water and gas in a cylindrical duct with an elliptical cross-section, considering a three-dimensional, isothermal and incompressible flow. For the numerical solution of the governing equations, the software Ansys FLUENT 15.0 was used. It was found that the lubrication provided by the water on the duct wall reduced the pressure variation by 7.20 times compared to the heavy oil single-phase flow, proving the good efficiency of the core-flow technique.