Hydrothermal alteration can create low‐permeability zones, potentially resulting in elevated pore‐fluid pressures, within a volcanic edifice. Strength reduction by rock alteration and high pore‐fluid pressures have been suggested as a mechanism for edifice flank instability. Here we combine numerical models of multiphase heat transport and groundwater flow with a slope‐stability code that incorporates three‐dimensional distributions of strength and pore‐water pressure to address the following questions: (1) What permeability distributions and contrasts produce elevated pore‐fluid pressures in a stratovolcano? (2) What are the effects of these elevated pressures on flank stability? (3) Finally, what are the effects of magma intrusion on potential flank failure in an edifice? Simulation results show that under a range of plausible parameters, water tables in a stratovolcano can be elevated or perched. These elevated water tables result in universally lower stability (lower factor of safety) compared with equivalent dry edifices, indicating a higher likelihood of flank collapse. Low‐permeability (<1 × 10⁻¹⁷ m²) layers such as altered pyroclastic deposits or breccias can result in locally saturated regions (perched water) and lower factors of safety near the ground surface but may actually reduce liquid water saturation and pore pressures in the core of the edifice and thus may favor small, shallow collapses over larger, deeper collapses. Magma intrusion into the base of the edifice increases pore‐fluid pressures and decreases the factor of safety. However, the shear strength of edifice rocks also exerts a significant control on stability, so both mechanical properties and pore‐fluid pressures are important for stability assessments.