Abstract: Based on the FGM Copula function, we describe the correlation between bivariate dependent survival data , and fit the marginal basic risk function by the B-spline function. We suggest a semiparametric bivariate dependent survival model, which is more flexible and has a wider range of adaptation than the full-parameter model. Based on the hybrid algorithm together with the Metropolis-Hastings algorithm within the Gibbs sampler, we propose a feasible Bayesian method simultaneously to estimate unknown parameters of interest, and to fit baseline survival functions. Meanwhile, we propose statistical diagnosis methods, including Bayesian data deletion influence analysis and Bayesian local influence analysis. Data simulation and example analysis demonstrate the feasibility of the proposed semi-parametric model, and the potential outliers or significantly influence can be detected by the proposed statistical diagnosis method.