The complete 3D nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The velocity field inside the pipe formulated using hydrostatic and Bernoulli equations. The hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in various time steps and the added inertia due to the hydrodynamic mass. Following the Newtonian derivation, the dynamics of the pipes element with effects of internal fluid are considered separately and the final governing set is derived by combining the equations of inertia equilibrium. The study focuses specifically on the effect of the inner flow to the global dynamics of the riser. This task is accomplished using time domain teachings and the Finite Element method is used as a powerful numerical method. Moreover the Euler-Bernoulli beam theory is used response to model the dynamic behavior of the flexible risers.