The development and revision of safety codes and standards for hydrogen infrastructure requires a solid scientific basis, including studies of unignited releases from high pressure systems for various scenarios. Most hydrogen releases are modeled as axisymmetric jets, but real leaks are more likely to be non-axisymmetric jets issuing from high aspect ratio cracks or slots. In the present study, underexpanded hydrogen jets from square and rectangular nozzles with aspect ratios of 1-16 were numerically modeled for stagnation pressures up to 20 MPa. The near and far flow fields were modeled separately using two sequential computational domains to accurately and efficiently capture the flow characteristics. The numerical models were first validated with experimental data from a previous experimental study and literature data. The mass fraction and velocity distributions show that the centerline decay rates increase as the nozzle aspect ratio increases, but this increase is dependent on the pressure. This means that the canonical decay law of round turbulent jets and plumes no longer applies to the slot nozzle jets for high pressures. The radial profiles collapse onto a Gaussian curve in the major axis plane, but neither collapse, nor are they Gaussian in the minor axis plane with peaks away from the jet centerline. Different shock patterns were identified along the major and minor axes and the axis switching phenomenon seen in the literature was also reproduced. The axis switching resulted in significantly wider flattened concentration distributions compared with the axisymmetric jet which may require consideration during safety analyses for non-circular nozzles. A scaling factor taking both the nozzle shape and pressure effects into account was then developed to better scale the centerline decay rates for jets from both the square and rectangular nozzles. The present study demonstrates that the nozzle shape effects on the jet spreading should not be overlooked and proper scaling factors are required to collapse the data and calculate decay rates. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.