We focus on the problematic of the intra-operative navigation during abdominal surgery, which requires an accurate registration of tissues undergoing large deformations. Such a scenario occurs in the case of partial hepatectomy: to facilitate the access to the pathology, e.g. a tumor located in the posterior part of the right lobe, the surgery is performed on a patient in lateral position. Due to the change in patient’s position, the resection plan based on the pre-operative CT scan acquired in the supine position must be updated to account for the deformations. We suppose that an imaging modality, such as the cone-beam CT, provides the information about the intra-operative shape of an organ, however, due to the reduced radiation dose and contrast, the actual locations of the internal structures necessary to update the planning are not available. To this end, we propose a method allowing for fast registration of the pre-operative data represented by a detailed 3D model of the liver and its internal structure and the actual configuration given by the organ surface extracted from the intra-operative image. The algorithm behind the method combines the iterative closest point technique with a biomechanical model based on a co-rotational formulation of linear elasticity which accounts for large deformations of the tissue. The performance, robustness and accuracy of the method is quantitatively assessed on a control semi-synthetic dataset with known ground truth and a real dataset composed of nine pairs of abdominal CT scans acquired in supine and flank positions. It is shown that the proposed surface-matching method is capable of reducing the target registration error evaluated of the internal structures of the organ from more than 40 mm to less then 10 mm. Moreover, the control data is used to demonstrate the compatibility of the method with intra-operative clinical scenario, while the real datasets are utilized to study the impact of parametrization on the accuracy of the method.