Numerical simulations are carried out for a highly under-expanded hydrogen jet resulting from anaccidental release of high-pressure hydrogen into the atmospheric environment. The predictions aremade using two independent CFD codes, namely CFX and KIVA. The KIVA code has beensubstantially modified by the present authors to enable large eddy simulation (LES). It employs a one-equation sub-grid scale (SGS) turbulence model, which solves the SGS kinetic energy equation toallow for more relaxed equilibrium requirement and to facilitate high fidelity LES calculations withrelatively coarser grids. Instead of using the widely accepted pseudo-source approach, the complexshock structures resulting from the high under-expansion is numerically resolved in a smallcomputational domain above the jet exit. The computed results are used as initial conditions for thesubsequent hydrogen jet simulation. The predictions provide insight into the shock structure and thesubsequent jet development. Such knowledge is valuable for studying the ignition characteristics ofhigh-pressure hydrogen jets in the safety context.Keywords : Hydrogen, under-expanded jet, Mach disk, large eddy simulation