Three-dimensional geometric models of the articular surfaces of the thumb carpometacarpal (CMC) joint were constructed using precise data obtained from stereophotogrammetry (SPG). It was demonstrated that by using a least-squares surface-fitting technique, the SPG data on the surface can accurately be described by a single parametric biquintic spline function. From this mathematical description, curvature maps of the surfaces were calculated for 13 CMC joints (eight females, average 64 yr old, five males, average 70 yr old). The surface geometry of each joint was analyzed, comparisons were made between trapezial and metacarpal surfaces of the joint and differences determined between males and females. With regard to joint surface areas, the female trapezium is significantly smaller than that of the metacarpal. The shape of the female trapezial surface is also fundamentally different from of males. No gender-related difference exists regarding the shape of the metacarpal surface. Congruence of the two opposing articular surfaces was defined by their relative principal curvatures. From these definitions, congruence in the radioulnar and dorsovolar anatomic directions, as well as the global congruence of the joint, were calculated. Most CMC joints were found to be more congruent along the radioulnar direction than the dorsovolar direction and, globally, female joints were found to be less congruent than male joints. The concept of joint congruence has played a central role in a number of hypotheses relating to the etiology of CMC joint osteoarthritis (OA), although conflicting hypotheses do exist. The precise quantitative findings of this study may lead to an improved understanding of CMC joint OA, and perhaps explain its prevalence in the female population over 55.