Degenerative changes of the intervertebral disc are among the most common causes of low back pain, where for individuals with significant symptoms surgery may be needed. One of the interventions is the total disc replacement surgery, where the degenerated disc is replaced by an artificial implant. For designing implants with good bone contact and continuous force distribution, the morphology of the intervertebral disc space and vertebral body endplates is of considerable importance. In this study we propose a method for the determination of the intervertebral disc space from three-dimensional (3D) computed tomography (CT) images of the lumbar spine. The first step of the proposed method is the construction of a model of vertebral bodies in the lumbar spine. For this purpose, a chain of five elliptical cylinders is initialized in the 3D image and then deformed to resemble vertebral bodies by introducing 25 shape parameters. The parameters are obtained by aligning the chain to the vertebral bodies in the CT image according to image intensity and appearance information. The determination of the intervertebral disc space is finally achieved by finding the planes that fit the endplates of the obtained parametric 3D models, and placing points in the space between the planes of adjacent vertebrae that enable surface reconstruction of the intervertebral disc space. The morphometric analysis of images from 20 subjects yielded 11:3 ± 2:6, 12:1 ± 2:4, 12:8 ± 2:0 and 12:9 ± 2:7 cm3 in terms of L1-L2, L2-L3, L3-L4 and L4-L5 intervertebral disc space volume, respectively.