Abstract This study addresses the muti-stage flowshop. There are more than one parallel machines in every stages. There is a limited buffer between two stages to store a limited number of jobs when the jobs are completed form the stage. Any job can be blocked at the stage while there was not enough space for storage. The objective measure of the problem is makespan. This problem was shown to be NP-hard. A heuristic procedure(Genetic Algorithm)that generates approximate efficient solution is presented and develop a steps with complete time. The results of the experimental investigation of the effectiveness of the algorithms are also presented.