In this research we aim to investigate the job shop scheduling problem with uncertain processing times. First we study the literature for the best solution approaches for the deterministic job shop problem. Among all developed algorithms in the literature the famous TSAB algorithm by Nowicki and Smutnicki in 1996 has shown well performance regarding the quality of solutions and CPU time. Then we develop and solve a two stage stochastic programming model, using TSAB and Sample Average Approximation technique, assuming the data are uncertain and associated with a well-known distribution. Furthermore, for more complex uncertainties we study robust and distributionally robust optimization techniques.