Estimating the motion between two bones is crucial for understanding their biomechanical function. The vertebral column is particularly challenging because the vertebrae articulate at more than one surface. This paper proposes a method to estimate 3D motion between two avian vertebrae, by bones surface reconstruction and contact modeling. The neck of birds was selected as a case study because it is a functionally highly versatile structure combining dexterity and strength. As such, it has great potential to serve as a source for bioinspired design, for robotic manipulators for instance. First, 3D models of the vertebrae are obtained by computed tomography (CT). Next, joint surfaces of contact are approximated with polynomial surfaces, and a system of equations derived from contact modeling between surfaces is established. A constrained optimization problem is defined in order to find the best position of the vertebrae for a set of given orientations in space. As a result, the possible intervertebral range of motion is estimated