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Pressure and stress perturbations associated with volcanic activity and geothermal production can modify the porosity and permeability of volcanic rock, influencing hydrothermal convection, the distribution of pore fluids and pressures, and the ease of magma outgassing. However, porosity and permeability data for volcanic rock as a function of pressure and stress are rare. We focus here on three porous tuffs from Krafla volcano (Iceland). Triaxial deformation experiments showed that, despite their very similar porosities, the mechanical behavior of the three tuffs differs. Tuffs with a greater abundance of phyllosilicates and zeolites require lower stresses for inelastic behavior. Under hydrostatic conditions, porosity and permeability decrease as a function of increasing effective pressure, with larger decreases measured at pressures above that required for cataclastic pore collapse. During differential loading in the ductile regime, permeability evolution depends on initial microstructure, particularly the initial void space tortuosity. Cataclastic pore collapse can disrupt the low‐tortuosity porosity structure of high‐permeability tuffs, reducing permeability, but does not particularly influence the already tortuous porosity structure of low‐permeability tuffs, for which permeability can even increase. Increases in permeability during compaction, not observed for other porous rocks, are interpreted as a result of a decrease in void space tortuosity as microcracks surrounding collapsed pores connect adjacent pores. Our data underscore the importance of initial microstructure on permeability evolution in volcanic rock. Our data can be used to better understand and model fluid flow at geothermal reservoirs and volcanoes, important to optimize geothermal exploitation and understand and mitigate volcanic hazards. Plain Language Summary: The volcanic rocks within a volcano or geothermal reservoir are frequently subject to changes in pressure and stress. Understanding whether pressures and stresses increase or decrease permeability, and by how much, is important for understanding volcano behavior and to maximize the efficiency of a geothermal reservoir. We performed experiments in which we measured the permeability evolution of porous volcanic rocks, three tuffs, as a function of pressure and stress. We also characterized their mechanical behavior. We first show that their mechanical behavior depends on composition: the more clay minerals and chlorite present, the weaker the tuff. We then show that increasing hydrostatic pressure (i.e., depth) decreases their permeability, but that differential loading in the ductile regime can either decrease or increase permeability. Rock permeability usually decreases during deformation in the ductile regime, and so the latter result is surprising. The observed differences in permeability evolution during ductile deformation is attributed to microstructural differences between the tuffs. However, changes in permeability as a function of pressure and stress are small when compared to other rocks, suggesting that tuff may help to maintain hydrothermal circulation in volcanoes and geothermal reservoirs, with attendant consequences for volcanic hazards and geothermal energy exploitation. Key Points: Tuffs are likely weakened by the presence clay minerals, chlorite, and zeolites due to a reduction in fracture toughnessPermeability of tuff decreases during hydrostatic pressurization, particularly following the onset of inelastic hydrostatic compactionPermeability of tuff can increase during ductile deformation due to flow‐parallel microcracks that form surrounding collapsed pores [ABSTRACT FROM AUTHOR]