The graph cut (GC) algorithm has emerged as an increasingly useful tool for many visual and image-processing problems in computing. This technique treats the segmentation problem as an energy minimization problem. Elastography is examined as a new application of ultrasound in medical diagnostic imaging. This method utilizes signals observed in different situations. Therefore, we expected to be able to apply the GC algorithm to elastography successfully. In this study, we examined the effectiveness of elastography using the GC algorithm. As a result, we obtained an appropriate displacement estimate for elastography using the GC algorithm.