The flow around a structure has been an important subject in wind engineering research. There are various kinds of unstable aerodynamic phenomena with regard to a bluff body. In order to understand the physical mechanism of aerodynamic and aeroelastic instability of a bluff body, the relations between the flow around structures and the motion of body with various section shapes should be investigated. Based on a series of wind tunnel tests, this paper addresses the aerodynamic stability of square cylinder with various corner cuts and attack angles in the uniform flow. The test results show that the models with corner cut produced generally better behaviour for the galloping phenomenon than the original section. However, the corner cut method can not prevent the occurrence of the vortex-induced vibration(VIV). It is also shown that as the attack angle changes, the optimum size of corner cut changes also. This means that any one specific size of corner cut which shows the best aerodynamic behaviour throughout all the cases of attack angles does not exist. This paper presents an intensive study on obtaining the optimum size of corner cut for the stabilization of aerodynamic behaviour of cylinders.