Developing critical software and ensuring its compliance with lawful requirements are difficult, expensive and resource-intensive activities. In the aeronautical industry, it is required to provide some quality guarantees in terms of robustness and functional safety. Documented guidance [1] to produce certifiable software describes the software life cycle processes and verification and validation activities. Among those guidelines, we would like to draw the attention on the need for a description of the functional behavior of the software. A test set for the validation and verification of the software is designed from this functional specification. To develop a test campaign, the test designer must ask him-or herself two questions: • Where to test? That is, which point in the software will be more likely to be badly implemented, i.e., which test case can allow us to detect an incorrect behavior. • How to reach that test case? That is, which configuration of the system under test will allow us to perform the verification of this test case. In order to implement specification based automatic test generation, we first formalize the functional behavior of the software by means of constraints programming [2] over interval variables. Then, with the help of interval constraint solving techniques [3], we describe a method to automatically achieve the two steps of specification based test design. First, we use a mutation testing approach [4] over interval constraints to evaluate the quality of the test set and generate new test cases.