Abstract: We propose bivariate Weibull regression model with heterogeneity (frailty or random effect) which is generated by compound Poisson distribution. We assume that the bivariate survival data follow bivariate Weibull of Hanagal . There are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births (both monozygotic and dizygotic) where genetic behavior (which is unknown and random) of patients follows a known frailty distribution. These are the situations which motivate to study this particular model. We propose two stage maximum likelihood estimation procedure for the parameters in the proposed model and develop large sample tests for testing no frailty and significance of regression parameters.