This paper describes a new approach to the problem of software testing. The approach is based on Bayesian graphical models and presents formal mechanisms for the logical structuring of the software testing problem, the probabilistic and statistical treatment of the uncertainties to be addressed, the test design and analysis process, and the incorporation and implication of test results. Once constructed, the models produced are dynamic representations of the software testing problem. They may be used to drive test design, answer what-if questions, and provide decision support to managers and testers. The models capture the knowledge of the software tester for further use. Experiences of the approach in case studies are briefly discussed.