Using the concept of extreme value theory and copula, this paper shows how to estimate association across financial markets. We select Peaks-Over-Threshold(POT) method and use Generalized Pareto Distribution(GPD) as the marginal distribution. We use the most popular used Gumbel copula as well as other three copulas. We fit these copulas to daily stock index returns of six countries and use upper and lower tail dependence to identify and quantify the tail dependence among stock returns.Empirical result show that asymptotic dependence exist between Asian-Pacific markets. And such extremal dependence become stronger after Asian Financial Crisis. But we failed to detect asymptotic dependence between US and Asian-Pacific markets.