In software testing practice, usually, the software under test (SUT) experiences multiple iterative processes of testing and modification. With the influence of many uncertain factors, such as defect distribution in the software under test, iterative developing and testing processes, and testers’ capabilities of defect detection, the software defect discovery process shows that the sequential characteristics correspond with test cycles, i.e. periodicity, random oscillation, and attenuation. Through a deep analysis of the basic characters and key influencing factors of the controlled software testing process, the paper proposes an Accumulative Bi-Damped Oscillation Model (ABDOM), which describes periodicity, random oscillation, and attenuation for a sequential software defect discovery process. It verifies ABDOM’s validity with defect data gathered from 2 true software test projects, and discusses the application scope of ABDOM and the possible applications in test predication and evaluation.