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Software testing represents one of the most explored fields of application of Search-Based techniques and a range of testing problems have been successfully addressed using Genetic Algorithms. Nevertheless, to date Search-Based Software Testing (SBST) has found limited application in industry. As in other fields of Search-Based Software Engineering, this is principally due to the fact that when applied to large problems, Search-Based approaches may require too much computational efforts. In this scenario, parallelization may be a suitable way to improve the performance especially due to the fact that many of these techniques are "naturally parallelizable". Nevertheless, very few attempts have been provided for SBST parallelization.In this paper, we present a Parallel Genetic Algorithm for the automatic generation of test suites. The solution is based on Hadoop MapReduce since it is well supported to work also in the cloud and on graphic cards, thus being an ideal candidate for high scalable parallelization of Genetic Algorithms. A preliminary analysis of the proposal was carried outaiming to evaluate the speed-up with respect to the sequential execution. The analysis was based on a real world open source library.