The stress characterization around the hole in a composite plate under tensile stress has been studied by the analytical method in this paper. The distribution of the stress components has been presented. With the Hashin Failure Criterion, the failure characterization and different failure modes by the analytical method and finite element method are then studied. The possibility of the failure in different modes is compared. It is found that the fiber breakage, matrix failure and delamination are dominant. The place of the failure is between 70 degree and 90 degree to the loading direction in this paper. The results from analytical method and finite element method can agree with each other. And they are all confirmed by the experiment results.