In this paper, the dynamic stability of simple supported shape memory alloy(SMA) pipe conveying fluid is studied.By applying the Hamiltons principle, the equation of motion is derived based on an improved Auricchio model.A solution for natural frequency and critical fluid velocity is presented by using the Galerkin Method.The effects of shape memory behavior, i.e.hysteresis-induced damping effect, variations of Youngs modulus, and several other system parameters on dynamic stability of SMA pipe conveying fluid are discussed.