Abstract: With light mass,small stiffness and low natural vibration frequency,membrane roofs are sensitive to wind.Generally,wind loading may induce large displacement and acceleration,of membrane roofs which may result in the change of local flow field around the structure and even induce the aeroelastic instability.So the wind-induced vibration of such structures should be analyzed considering the wind-structure interaction.The determination of the critical wind velocity is one of the main targets.The critical wind velocity of a hyperbolic paraboloid membrane roof with rectangular plane under the action of uniform ideal potential flow is studied.The equilibrium equation of the membrane roof is obtained.The potential flow theory in fluid mechanics is adopted to define the aerodynamic forces on the membrane roof and the equation of wind-structure interaction is obtained.The Bubnov-Galerkin method is applied to transform this complicated interaction equation into a system of second order linear differential equations with constant coefficients.Finally,Routh-Hurwitz stability criterion is used to determine the critical wind velocity.The formula shows that the critical wind velocity depends on the material parameters,the scale and the shape of the structure,and the pretension forces in two principal directions.