Software-as-a-Service (SaaS), a new software delivery model, plays an important role in daily life. In SaaS, mission-critical applications are composed, deployed, and executed on cloud platforms. SaaS applications needed to have high reliability and availability before publishing. Testing SaaS applications becomes important, as the large number of testing prior to their deployment. Test Algebra (TA), a algebraic system, identifies faults in combinatorial testing for SaaS applications using existing test results and eliminates those related faults. Although TA eliminates a large number of configurations from considerations, it is still difficult to finish testing enormous combinations of services in a reasonable time. To improve TA analysis, this paper proposes a concurrent TA analysis. It allocates workloads into different clusters of computers and performs TA analysis from 2-way to 6-way configurations. Different database designs are used to store the test results of various configurations. Faulty and operational table search algorithms are proposed to retrieve existing test results. One 25-component experiment is simulated using the proposed solutions. The same experiment is also simulated on multiple processors for concurrent TA analysis.