A prerequisite to biomedical analyses of the right ventricular free wall (RVFW) is the characterization of its in vivo geometry and instantaneous wall thickness (WT). We present a method to reconstruct and mathematically model the in vivo RVFW surface geometry using ECG-gated magnetic resonance imaging (MRI). From digitized contours we reconstructed the endo- and epicardial surfaces of the entire heart, and approximated the RVFW surface geometry by local biquadric surface patches. An insurface coordinate system was developed, with respect to which the metric tensor, curvature tensor, major (k2), and minor (k1) principal curvatures were computed. The method was evaluated using MRI data from one dog, which showed that k2 was about 10 times k1, with k2 and k1 approximately perpendicular and parallel to the RV long axis, respectively. During systole, k1 and both principal curvature directions remained essentially unchanged, while k2 revealed only a 7% decrease (rho < 0.05) in the sinus region. These results suggest that while the RVFW undergoes small changes in surface geometry during systole, its overall curvature remained constant. The WT/mean radius of curvature ratio was less than 0.1 during systole throughout the RVFW, indicating it can be idealized as a thin shell.