This paper presents a method for real-time augmentation of vascular network and tumors during minimally invasive liver surgery. Internal structures computed from pre-operative CT scans can be overlaid onto the laparoscopic view for surgery guidance. Compared to state-of-the-art methods, our method uses a real-time biomechanical model to compute a volumetric displacement field from partial three-dimensional liver surface motion. This permits to properly handle the motion of internal structures even in the case of anisotropic or heterogeneous tissues, as it is the case for the liver and many anatomical structures. Real-time augmentation results are presented on in vivo and phantom data and illustrate the benefits of such an approach for minimally invasive surgery.