With the stringent emission regulations and renewable energy concerns, hydrogen application either to direct injection combustion or fuel cell application attracts more attention. However, a major obstacle for vehicle utilization of hydrogen as a main fuel is onboard storage. Due to the low mass density, hydrogen has the lowest energy per unit volume among all potential fuels. One of the typical methods to store hydrogen is in very high pressure storage tanks. The high pressure (35 MPa and higher) combined with small size of hydrogen molecules makes the tanks and adjacent fittings prone to leakage, which may cause important potential safety issues, given the wide combustion range and easy ignition of hydrogen. Our research focuses on characterizing the relative importance of basic modes of hydrogen leakage at the joints of commercial stainless steel fittings. Two types of fittings that include National Pipe Thread Standard (NPT) screw treads and standard compression fitting ferrules are modeled as a capillary duct with the same hydraulic diameter (height of the duct). The flow rate through the contacting faces is determined and correlated to the differential pressure drop, thread treatment, torque, and temperature. The analytical models from the viscous flow regime to free-molecular flow regime are derived. We compare the analytical formulation in the slip flow regime with previous experimental results for nitrogen and helium, and then apply this analytical model to predict the hydrogen leakage at the high pressure ratio condition. An experiment extending these results to hydrogen is also reported in the paper, and the results are compared with the analytical prediction.