Testing is process to detect the fault. This thesis proposes a design of the test point insertion for testing quasi-delay insensitive (QDI) asynchronous circuits that use stuck-at fault model. Test point insertion is one process in testing process by using control point and observe point for increasing fault coverage of the circuit. In asynchronous circuits testing process, we use stg-like diagram for showing circuit behavior and apply stable state graph (SSG) for decreasing complex of circuit behavior. We use stable state graph and extend stable state graph (ESSG) for increasing fault coverage of the circuits. Experiments on the benchmark circuits show that test point insertion can detect all permanent stuck-at faults.