Abstract: The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures.