In this paper, we carry out robust modeling and influence diagnostics in Birnbaum‐Saunders (BS) regression models. Specifically, we present some aspects related to BS and log‐BS distributions and their generalizations from the Student‐ t distribution, and develop BS‐ t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.