Much of the hand's functional capacity is due to the versatility of the motions at the thumb carpometacarpal (CMC) joint, which are presently incompletely defined. The aim of this study was to develop a mathematical model to completely describe the envelope of physiological motion of the thumb CMC joint and then to examine if there were differences in the kinematic envelope between women and men. In vivo kinematics of the first metacarpal with respect to the trapezium were computed from computed tomography (CT) volume images of 44 subjects (20M, 24F, 40.3 ± 17.7 yr) with no signs of CMC joint pathology. Kinematics of the first metacarpal were described with respect to the trapezium using helical axis of motion (HAM) variables and then modeled with discrete Fourier analysis. Each HAM variable was fit in a cyclic domain as a function of screw axis orientation in the trapezial articular plane; the RMSE of the fits was 14.5 deg, 1.4 mm, and 0.8 mm for the elevation, location, and translation, respectively. After normalizing for the larger bone size in men, no differences in the kinematic variables between sexes could be identified. Analysis of the kinematic data also revealed notable coupling of the primary rotations of the thumb with translation and internal and external rotations. This study advances our basic understanding of thumb CMC joint function and provides a complete description of the CMC joint for incorporation into future models of hand function. From a clinical perspective, our findings provide a basis for evaluating CMC pathology, especially the mechanically mediated aspects of osteoarthritis (OA), and should be used to inform artificial joint design, where accurate replication of kinematics is essential for long-term success.