Abstarct: Nowadays, reliability and performance of the systems are the most important principles in using systems. Our goal is the estimation of the system reliability in two cases, parallel and series systems, in stress-strength models. Therefore, we estimated the system reliability given the independence of the components (strength) under different distributions (Exponential, Weibull, Gamma, Pareto,...) by maximum likelihood and Bayesian approach in order to achieve better estimates, useful results and to raise working efficiency. The results are compared for some cases. In addition to the estimation of reliability, we derive the estimator distributions. Also, we simulated some of estimators to get optimal estimator. Under some of distributions, the estimator of reliability has complex form. So in such cases for simulating, using the Monte Carlo Markov Chain (MCMC) sampling method is recommended.