The relative excess odds or risk due to interaction (ie, RERIOR and RERI) play an important role in epidemiologic data analysis and interpretation. Previous authors have advocated frequentist approaches based on nonparametric bootstrap, the method of variance estimates recovery, and profile likelihood for estimating confidence intervals. As an alternative, we propose a Bayesian approach that accounts for parameter constraints and estimates the RERIOR in a case-control study from a linear additive odds-ratio model, or the RERI in a cohort study from a linear additive risk-ratio model. We show that Bayesian credible intervals can often be obtained more easily than frequentist confidence intervals. Furthermore, the Bayesian approach can be easily extended to adjust for confounders. Because posterior computation with inequality constraints can be accomplished easily using free software, the proposed Bayesian approaches may be useful in practice.