The process of volcano-ground ice interaction on Mars is investigated by thermodynamic calculations and observations of Viking Orbiter images. We develop a numerical model of volcano-ground ice interaction that includes heat transport by conduction, radiation from the surface, heat transfer to the atmosphere, and H₂O phase changes in an ice-rich permafrost. We consider eruption of lava flows over permafrost, and intrusion of sills into permafrost. For eruption of lava over permafrost, most of the heat in the flow is lost by radiation and atmospheric effects. The amount of H₂O liquid and vapor produced is small, and its removal would not be sufficient to cause collapse that would lower the surface of the lava flow below the surrounding terrain. For intrusion of a sill, most of the heat in the sill eventually goes into H₂O phase changes, producing much larger amounts of water that could have profound geomorphic and geochemical effects. Approximate meltwater discharge rates are calculated for both extrusive and intrusive interactions. We examine two large regions of large-scale volcano-ground ice interactions. Near Aeolis Mensae, intrusion of a complex of dikes and sills into ice-rich ground has produced substantial melting, with mobilization and flow of material. This interaction probably also produced large quantities of palagonite tuff and breccia. Morphologic evidence for progressive fluidization implies that meltwater was stored beneath the surface for some time, and that most of the release of water and volcanic mudflow took place late in the interaction. Northeast of Hellas, several large channels emanate from the area near the volcano Hadriaca Patera. If genetically related to the volcanic activity, large collapse features at the sources of some channels must have originated due to heat from large buried magma bodies. A channel emerging directly from the base of Hadriaca Patera may have originated from release of heat from thick extruded material. Other small channels in the region results from heat released from surface lava flows. Inferred channel discharges may be compared to discharge rates calculated for lava-ground ice interactions. Such comparisons show that meltwater probably accumulated beneath the surface and then was released rapidly, with a discharge rate limited by soil permeability. Volcano-ground ice interaction has been a widespread and important geologic process on Mars, and may be the primary source of palagonites making up the ubiquitous Martian dust.