It is the first part of a two-part study devoted to deriving threedimensional (3-D) motion equations of a cantilevered pipe discharging fluid at sea. The 3-D nonlinear equations were derived based on the modified Hamiltons principle. The Morison formula was used to calculate the external fluid-induced static drag force and viscous damping forces in the in-line (IL) and cross-flow (CF) directions. A double-van der Pol oscillator model was employed for the Vortexinduced vibrations (VIVs). The derived mathematical model employing wake coefficients in Facchinetti et al. (2004) and solution methods were validated by comparisons of blind numerical predictions with experimental results.