The stability of a supported cylinder subjected to axial flow is studied numerically. The dynamics of the cylinder is investigated with the numerical method applying the new nonlinear model in witch the nonlinear terms considered are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using three-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder. Some integration terms that appear in the discretization of the equation and can not be expressed in an analytical form are calculated using a numerical method. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence and at a higher velocity the flutter around the zero equilibrium may occur. There is some region in witch three different motions (configurations) can take place at the same parameter values.