In this paper, the stability and nonlinear dynamics are studied for a slender flexible cylinder subjected to axial flow. A nonlinear model is presented, based on the corresponding linear equation of motion, for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are only the additional axial force induced by the lateral motions of the cylinder. Using six-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain, with this relatively simple nonlinear model, the flutter instability found in experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. As the flow velocity increases further, the quasiperiodic motion around the buckled position occurs, and this evolves into chaotic motions at higher flow.