Generalized Differential Quadrature Rule(GDQR)was applied to investigate the stability of a pipe conveying fluid on an elastic foundation. Based on the motion equations and boundary conditions of a pipe conveying fluid, the matrix eigenvalue equation consisted of the dynamic equations and boundary conditions was obtained after discreted by GDQR. After analyzing the corresponding eigenvalue equations,the results of critical velocity for divergence and flutter under different supporting conditions were calculated ,the effect of translational and rotational spring stiffness to critical instability velocity and stability region was discussed , meanwhile the influence of mass ratio ,reaction coefficient and shear modulus in two-parameter model to stability region were studied, some useful conclusions were obtained. The conclusion of the study could provide some useful suggestion for engineering.