Abstarct: Some regression models have a large number of explanatory variables,where, it is suggested to use penalized methods for estimation. Among these methods, the LASSO simultaneously selects the variables and estimates the parameters of the regression model. Now, from Bayesian view point, we can use Bayesian penelized methods. In this modeling, the prior distribution is usually chosen in such a way that the resultant is similar to one of the penalty estimators in classical models. In this dissertation, we study the Bayesian penalized regression and examine Bayesian LASSO and Bayesian horseshoe approaches in more details. For performance evalvation of the Bayesian penalized regression, we analyze two diabetes data sets.