In this paper we introduce a bivariate modified odd generalized exponential linear failure rate (BMOGELFR) distribution. The cumulative distribution function of this bivariate model has absolutely continuous and singular parts. Representations for the cumulative and density functions are presented and properties such as marginal, conditional distributions and some reliability measures, the joint reliability function, joint hazard rate, and joint reversed (hazard) function. The estimation of the parameters by maximum likelihood is discussed and the Fisher information matrix is determined. An applications to real data is carried out to illustrate that the new distribution is more flexible and e¤ective than other popular distributions in modeling lifetime data. Finally, some simulations are presented to verify the performance of the direct maximum-likelihood estimation.