This paper studies the modeling method and application of M-Copula model. The EM algorithm is used to estimate the parameters of M-Copula model, and the corresponding statistical results are obtained. We adopt M-Copula model to analyze the correlation between Shanghai Composite Index and Shenzhen Composite Index. By analyzing the characteristics of the two sample data, the GARCH-$t$ model is used to establish the marginal distribution model of its; and according to the correlation characteristics between two sequence of logarithmic return rates, the M-Copula model is adopted to model and analyze its related structure. Because M-Copula integrates the characteristics of different single Copulas, it has more flexible distribution forms and more prominent ability to describe the fat tails and correlation characteristics of data, and more importantly, the effect is better than the single Copula.