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We present a theory for the motion of water vapor at depth in a discretely fractured permeable medium induced by atmospheric barometric pressure fluctuations, or ’barometric pumping’. The theory involves multiphase mass and energy transport in a fracture/matrix system, with discrete representation of the fracture system. The barometric pressure fluctuations are approximated as periodic in time, with amplitude corresponding to measured values. To simplify the analysis, a ’single-horizon’ approximation is applied in which the time-mean gradient is used to evaluate the vertical advective flux in the fractures. Time-periodic solutions are obtained numerically, enabling the calculation of the net efflux of moisture per cycle. The model is applied to material representative of the Yucca Mountain region of southwestern Nevada. The results indicate that the efflux of moisture carried upward from significant depths by barometric pumping is much less than the near surface efflux that is commonly estimated by assuming that air enters the medium dry and is returned to the atmosphere fully saturated with water vapor. This near surface efflux consists primarily of moisture discharged from the upper layer which is frequently replenished by precipitation. Of greater interest to nuclear waste repository design and estimations of net infiltration in arid regions is the fraction of the total moisture efflux that comes from significant depths. This deep transport is quantified by the fracture/matrix transport model described here. Although the transport by barometric pumping from depth is small compared to the total moisture expelled from the surface layer, it is an order of magnitude greater than the vertical moisture flux carried from depth by diffusion.