This paper presents preliminary results of an aeroelastic wind tunnel test on a cable dome. The structural design of the model is given in detail. Similarity requirements based on dimensional analysis are discussed, including Froude number, Cauchy number, and Scruton number. Structural tests are conducted on the aeroelastic model. Dynamic instability subject to harmonic excitation like a single-degree-of-freedom hardening system is verified. Both odd and even frequency components are excited when the shaking table shakes at . For the one-degree-of-freedom Duffing model, even frequency components will be impossible due to the symmetry of the motion equation if symmetry-breaking bifurcation behaviors do not occur. Phase plane is checked and discussed when the shaking table shakes at . A strange attractor appears to exist on the basis of the Poincare map. Some statistical results of wind tunnel tests are presented. The possibility of aeroelastic instability of the cable dome is discussed.