The paper proposes a 3D non-linear reduced order model for a Cantilevered Pipe Conveying Fluid under VIV. The Modular Modeling Methodology (Orsino, 2017), has been successfully applied for the non-linear modeling - both FEM and reduced order models - of a cantilevered pipe ejecting fluid and free to oscillate in a vertical plane (Orsino and Pesce, 2017). The same strategy has been also used for the derivation of an extended non-linear reduced order model which includes the simultaneous effects of VIV, by adapting wake-oscillator model to the flexible pipe case (Orsino, Pesce and Franzini, 2017). The objective of the present paper is to go even further, by extending the formulation to a three-dimensional model. VIV effects are now modeled with a two degree-of-freedom wake oscillator. A linear stability analysis is carried out having the reduced velocities of the internal and external flows as control parameters. Numerical simulations are performed with the non-linear model in the neighborhood of possibly existing bifurcations, illustrating the discussion on the dynamic response of this system. Interesting dynamic behaviors are observed, regarding the coupling effects of external and internal flows.