This paper is concerned with the detection and characterization of material loss within lap joints. One of the most commonly used nondestructive methods to inspect lap joints is the eddy current method [1]. In this technique, the percentage of material loss is determined by comparing the signal from the defective joint with a reference signal. Ultrasonic tests based on pulse-echo technique can also be used to detect thickness reduction in lap joints. However both of these methods require that the sensor be directly above the defects, thus making their practical implementation extremely time consuming. Improving the efficiency of lap joint inspection is one of the most critical tasks currently facing the NDE community. In this paper we discuss the feasibility of using an ultrasonic technique based on guided waves launched across the lap joint. It is well known that the characteristics of guided waves can be used to detect defects in plates [2]. The geometry of the lap joint makes it much more difficult to extend the guided wave based method to lap joints. There is no closed form solution to the problem of wave propagation across lap joints. Due to the change of thickness and the existence of vertical stress free boundaries, nonpropagating modes may play an important role inside and near the overlapped region. With material loss inside the lap joint, the geometry becomes even more complicated. Thus the problem of wave propagation in the lap joint can only be solved by numerical and experimental methods.