Abstract: The traditional method of flood frequency analysis based on univariate distribution is unable to consider the dependence structure between flood characteristics. This paper focuses on the calculation of return periods and design values of bivariate floods using the theory of Kendall return period. We have applied this calculation method to flood analysis for the Zhaoshiyao and Suide stations of the Wudinghe basin in North Shaanxi, using a bivariate Frank Copula to describe the joint distribution of flood peak and flood volume. To find the most appropriate values of design floods, a component-wise excess method and maximum likelihood method are adopted on three definitions of the return period: joint return period, co-occurrence return period, and Kendall return period. The results indicate that the design values calculated using both methods have no considerable difference, and that the design values on these definitions are the largest, intermediate and the smallest respectively. An examination on the three definitions shows that the former two distinguish dangerous regions by variable values. Both have a certain fault, but they can be applied satisfactorily in some specific cases. The latter makes the distinguishment by joint probability, thus avoiding overestimation or underestimation of the dangerous regions. Therefore, Kendall return period is recommended in general cases.