This article analyzes a realistic kinematic model of the trapezio-metacarpal (TM) joint in the human thumb that involves two non-orthogonal and non-intersecting rotation axes. The estimation of the model parameters, i.e. the position and orientation of the two axes with respect to an anatomical coordinate system, was carried out by processing the motion of nine retroreflective markers, externally attached to the hand surface, surveyed by a video motion capture system. In order to compute the model parameters, prototypical circumduction movements were processed within an evolutionary optimization approach. Quality and reproducibility in assessing the parameters were demonstrated across multiple testing sessions on 10 healthy subjects (both left and right thumbs), involving the complete removal of all markers and then retesting. Maximum errors of less than 5 mm in the axis position and less than 6 degrees in the orientation were found, respectively. The inter-subject mean distance between the two axes was 4.16 and 4.71 mm for right and left TM joints, respectively. The inter-subject mean relative orientation between the two axes was about 106 and 113 degrees for right and left TM joints, respectively. Generalization properties of the model were evaluated quantitatively on opposition movements in terms of distance between measured and predicted marker positions (maximum error less than 5 mm). The performance of the proposed model compared favorably with the one (maximum error in the range of 7-8 mm) obtained by applying a universal joint model (orthogonal and intersecting axes). The ability of in vivo estimating the parameters of the proposed kinematic model represents a significant improvement for the biomechanical analysis of the hand motion.