Based failure criteria of composite materials structural damage and simulation of finite element dynamic impact, the drop process and damage failure of composite cylinder are calculated and analysed. For composite cylinders with different wind angles falling from a height, the stresses of internal points during the impact process are obtained. Based on the value of the process stress, the failure of the cylinder is analysed. The results show that at the moment when the cylinder bounces back after impacted with the ground, the stress and strain reaches to the maximum. The maximum hoop stresses are at cylinder mouth and cylinder bottom which collide with ground. Maximum axial tensile stresses are at the central body of cylinder. The stress distribution of 13 degrees fiber angle of cylinder is slightly less than that of 25 degree. By Tsai-Wu composite failure criterion, there is no failure of the composite cylinder.