In noninvasive high intensity focused ultrasound (HIFU) treatment, we often need to register MR images acquired with different patient positioning or at different respiratory instances. In these scenarios, the abdominal organs such as the liver exhibit a large motion in different images. In our previous work, we proposed a fast neuro-fuzzy technique for deformable registration with small motion. In this study, based on elastic solid mechanics, we extend our previous results to deformation with large motion which is often the case for soft tissues in HIFU treatment. The proposed method involves minimizing strain energy of soft tissues which is constrained by 3D curves of blood vessels and point marks. It provides fast and robust deformable match for internal structures such as blood vessels, and eliminates local minima. Furthermore, the strain energy constraint provides good generalization properties, prevents the issue of overfitting, and leads to physically consistent deformable registration results. We have demonstrated the effectiveness of our deformable technique in registering MR liver images. Validation shows a target registration error of 2.31 mm and an average centerline distance error of 2.30 mm. This technique has the potential to significantly improve the registration capability and the quality of intra-operative image guidance in HIFU procedures.