Analytical and numerical solutions are developed to simulate the pressurization, expansion, and flow of groundwater contained within saturated, intact host rocks subject to sudden heating from the planar surface of an igneous intrusion. For most rocks, water diffuses more rapidly than heat, assuring that groundwater is not heated along a constant-volume pressure path and that thermal expansion and pressurization adjacent to the intrusion drives a flow that extends well beyond the heated region. The forcing parameter for pressurization and flow is α ΔT, where α is a thermal expansion coefficient reflecting the overall expansion of water heated through the temperature difference ΔT between the initial ambient and intrusive values. Pore pressure increases due to heating are greatest when the intrusion is emplaced rapidly and where the intrusive contact is impervious to groundwater contained in stiff, impermeable rocks with high thermal diffusivities and porosities. The maximum velocity of water flowing in pores decays with the inverse square root of time and is insensitive to hydraulic properties of the host rocks. Pressures are lessened and flow directions are reversed with the onset of hydrothermal convection. This occurs at times ranging from hours to weeks after onset of intrusion. As magma rises into near-surface rocks, steam can be generated. Solutions indicate that pressure increases and velocities are sensitive to the overall amount of expansion rather than the behavior of the water-steam transition. Both the overall thermal expansion coefficient α and the temperature difference ΔT are greater in shallow (<1 km) environments than in deep (~5 km) ones. Thus, for rocks with similar transport properties, pressure increases, due to heating are greatest in shallow environments. Although solutions can be applied to rocks with a wide variety of properties, pressure increases are calculated for compliant quartz-rich sedimentary rocks with a porosities between 1 and 20% and permeabilities between 1 darcy and 1 μdarch, subject to temperature increases of 500 and 1000 K at depths ranging from 0.1 to 5 km in a region of hydrostatic pressures and normal geothermal gradient. Such rocks, with porosities greater than 5%, permeabilities less than a 0.1 mdarcy, and drained hydrostatic compressibilities of 10-4/MPa, undergo pressure increases greater than 10 MPa (100 bars) for conditions typical of water table depths of 2.5 km and heating to 500 K above ambient. Similar rocks, but with permeabilities less than 1 mdarcy, undergo pressure increases of 10 MPa for conditions typical of 1 km water table depth. Rocks commonly considered to be good aquifers undergo pressure increases of less than 1 MPa, primarily because of their high permeability. Although these estimates neglect the effects of fracturing and brecciation that may accompany such pressure increases, calculations indicate that pressure increases due to heating of cool groundwater can lead to failure of host rocks by a phreatic mechanism.