Dynamics analysis of the rotational axially moving pipe conveying fluid under simply supported condition investigated in this research. The pipe assumed as Euler Bernoulli beam. The gyroscopic force and mass eccentricity were considered in the research. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The non-dimensional equations were discretized via Galerkin’ method and were solved using Rung Kutta method (order 15s). The frequency response curve obtained in terms of non-dimensional rotational speed. The bifurcation diagrams are represented in the case that the non-dimensional fluid speed, non-dimensional axial speed and non-dimensional rotational speed were respectively varied and the dynamical behavior is numerically identified based on the Poincare' portrait. Numerical simulations indicated that the system response increases by increasing non-dimensional axial speed of the pipe, non-dimensional fluid speed and non-dimensional rotational speed of the pipe and then decreases after passing critical area. The system is unstable at critical point associated with non-dimensional axial speed. Poincare portrait indicates periodic motion in transverse vibrations of the pipe at some points of control parameters. Phase portrait and FFT (Fast Fourier Transform) diagrams were used for validation of the results.