We present a three-dimensional modeling study of gas flow in the unsaturated fractured rock of Yucca Mountain. Our objective was to estimate large-scale fracture permeability, using the changes in subsurface pneumatic pressure in response to barometric pressure changes at the land surface. We incorporate the field-measured pneumatic data into a multiphase flow model for describing the coupled processes of liquid and gas flow under ambient geothermal conditions. Comparison of field-measured pneumatic data with model-predicted gas pressures is found to be a powerful technique for estimating the fracture permeability of the unsaturated fractured rock, which is otherwise extremely difficult to determine in field studies with large scales of interest. In addition, this study demonstrates that the multidimensional flow effect on estimated permeability values is significant and should be included when determining fracture permeability in heterogeneous fractured media.