In this paper, we propose a bivariate distribution for the bivariate survival times based on Farlie-Gumbel-Morgenstern copula to model the dependence on a bivariate survival data. The proposed model allows for the presence of censored data and covariates. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated via a simulation study and a real dataset.Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Engenharia de Produção, Faculdade de Engenharia de Bauru, Bauru, Av. Eng. Luiz Edmundo C. Coube 14-01, CEP 17033-360, SP, BrasilUniversidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Engenharia de Produção, Faculdade de Engenharia de Bauru, Bauru, Av. Eng. Luiz Edmundo C. Coube 14-01, CEP 17033-360, SP, Brasil