With the rapid development of financial industry, copula methods are more and more widely used for the study of financial fields. By selecting the appropriate copulas, the tail dependence of financial variables can be measured easily. Using the nonparametric estimation method to select A12 copula from Archimedean copulas, and do tail dependence study of SSE composite index and SESE component index. The results show that the SSE composite index and SESE component index simultaneously have the upper tail dependence and lower tail dependence, and the upper tail dependence coefficient is less than the lower tail dependence coefficient, which is consistent with the real financial market rule.