<p>Modal regression focuses on the most likely values of the response variable given the regression variables, thereby uncovering important structures that may be overlooked by traditional regression approaches. In practical applications, prior knowledge can be incorporated into the model as constraints, which restrict the parameters space and improve the accuracy of parameter estimation. To this end, we propose Bayesian modal regression models with linear inequality constraints. Based on a flexible Gumbel distribution and a two-piece scale Student-t distribution, we develop two MCMC sampling algorithms for the parameter estimation. Simulation studies demonstrate that the proposed methods with linear inequality constraints yield lower root mean square errors in parameter estimation and produce narrower prediction intervals compared to their unconstrained counterparts. Furthermore, we demonstrate the effectiveness of proposed methods by applying to real-world murder rate data.</p>