This paper implementations of parallel Tabu Search algorithms for solving the problem of scheduling nonpreemtable, independent jobs on parallel, identical machines to minimize the makespan are presented. F our different types of parallel Tabu Search based on Michael J. Flynn , s computer architectural classification scheme are considered. A computational experiment is described performed in two different parallel computer architectures: multiprocessor scalar system with shared memory and scalable supercomputing system with distributed memory .A comparison of results obtained for sequential versions of the algorithm as well as parallel ones in both the architectures is presented. Some conclusions and final remarks are included.