Fluid flows in consolidated porous media of volcanic origin are being investigated to support such diverse efforts as the modeling of thermal/outgassing phenomena at Mount St. Helens and the hydrological modeling of tuffaceous rocks in support of the Department of Energy’s (DOE) Nevada Nuclear Waste Storage Investigations Project An experimental apparatus was designed and built to allow water-saturated permeabilities as low as 10−18 m2 to be measured on cores of diameter 5 cm and length 10 cm under steady-state flow conditions. This same apparatus can also be utilized in a transient (pressure-decay) mode in order to measure permeabilities several orders of magnitude lower than the steady-state limit. Tests were conducted on samples of pumice, fractured welded tuff, and welded tuff, representing a permeability range of seven orders of magnitude Pumice was found to have a permeability of ∼3×10−12 m2, sufficiently high to allow the complete Darcy-to-Ergun regime to be investigated Welded (unfractured) tuff was tested in the transient mode, yielding a permeability of ∼5×10−19 m2. Two, long-time-scale, steady-flow experiments were conducted on a core of welded tuff containing a single, through-going fracture. For the first experiment, the core was an integral cylinder containing a naturally occurring fracture. For the second experiment, the core was separated into two pieces along the existing fracture plane, then rejoined. Effects of essentially constant, as well as rapidly varied, circumferential stress were studied in both tests. Results showed core permeability to decay to 2×10−18 m2 in both cases, independent of the initial fracture state (closed versus open). With a naturally occurring fracture, core permeability decreased by a factor of 2 over a 200-h test period. With an initially open fracture, core permeability decreased by a factor of 4 under the influence of a comparable 200-h load-time history, after 700 h of testing, core permeability was reduced by an order of magnitude from its initial level. Final effective hydraulic fracture aperture was calculated to be 10−6 m, corresponding to a calculated effective fracture permeability of 10−13 m2 Fracture flow was thus estimated to account for 80% of the total flow rate through this core under final test conditions.