In this paper, we propose Multiple-Surface Active Volume Models (MSAVM) to extract 3D objects from volumetric medical images. Being able to incorporate spatial constraints among multiple objects, MSAVM is more robust and accurate than the original Active Volume Models [11]. The main novelty in MSAVM is that it has two surfacedistance based functions to adaptively adjust the weights of contribution from the image-based region information and from spatial constraints among multiple interacting surfaces. These two functions help MSAVM not only overcome local minima but also avoid leakage. Because of the implicit representation of AVM, the spatial information can be calculated based on the model's signed distance transform map with very low extra computational cost. The MSAVM thus has the efficiency of the original 3D AVM but produces more accurate results. 3D segmentation results, validation and comparison are presented for experiments on volumetric medical images.