Abstract: Abstract Computational methods for simulating and predicting progressive fracture in composite structures are the current important research subject in composite community and these researches are of significant practical use. The fundamental principles of the progres-sive damage models and the state-of-the artreview of these methods are presented. Furthermore, two types of interface elements, spring interface elements and six-noded interface elemenu, which are developed by the present author and can be used to predict delamination failure of composites, are introduced in detail. Many examples are provided which show good agreement between theoretical predictions and experiments. These examples indicate that it is very possible to simulate the progressive fracture of cxunposite structures with a computer.