In this paper, we discuss a regression model based on the bivariate Birnbaum–Saunders distribution. We derive the maximum likelihood estimates of the model parameters and then develop associated inference. Next, we briefly describe likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. Monte Carlo simulations are then carried out to examine the performance of the estimators as well as the interval estimation methods. Finally, a numerical data analysis is performed for illustrating all the inferential methods developed here.