Numerical solutions are obtained for the ascending convection of ground water with boiling. The results are applicable to geothermal reservoirs above cooling igneous intrusions. The steady vertical flow of water in a uniform permeable medium is assumed. Pressure release boiling results in a two-phase, steam-water zone. Within this zone, steam percolates upward relative to water. Near the surface is a water zone due to conductive cooling. The conductive cooling prevents boiling at low water flow rates. Calculated results are compared with temperature and pressure logs from drill holes in the thermal systems of Steamboat Springs, Nevada, and Yellowtone National Park, Wyoming.