Abstract: This paper deals with the vibration and the aerodynamic stability of small curvature membrane in uniform flow. Applying the linear airfoil theory and treating the air flow as two-dimensional ideal potential flow, the characteristic equation of membrane vibration is deduced by simulating membrane figure with traveling wave. Then instability type and phase of membrane is investigated. In order to determine critical wind velocity of membrane at first order instability, further vortex sheet on membrane is used to substitute the infinitesimal thickness boundary layer between wind and membrane surface. Expression of aerodynamic force is obtained; meanwhile, finite sinusoidal waveform is employed to simulate kinetic shape of membrane approximately. The maximum amplitude of membrane vibration is solved based on Hamilton principle and Newton's iterative method. The wind velocity of first order instability is obtained from the dynamic equilibrium relationship between aerodynamic force with dead weight and inertia force of membrane.