Testing a group of software artifacts that implement the same specification can be time consuming, especially when the test case repository is large. In the meantime, some test cases may cover the same aspects in the software, thus it is not necessary to apply all the test cases. This paper proposes a Model-based Adaptive Test (MAT) case selection and ranking technique to eliminate duplicate test cases, i.e., test cases with the similar coverage, and rank the test cases according to their potency and coverage. This technique can be applied in various domains where multiple versions of applications are available to test, such as web service testing, n-version applications, regression testing, and standard-based testing. The MAT is based a statistical model based on earlier testing results, and the model can determine the next sets of test cases to minimize the testing effort. The MAT is then applied to testing of multi-versioned web services and the results shows that the MA T can reduce testing effort while still maintain the effectiveness of testing.