Field observations indicate that dikes form and grow in magma source regions, but the mechanics of this process are poorly understood. I derive time-dependent and self-similar solutions for the growth of buoyant dikes fed by porous flow in partially molten rock. The host rock is treated as poroelastic; for basaltic (but not rhyolitic) dikes, large-scale viscous deformation of the rock is insignificant for dikes large enough to meet the classical Griffith fracture criterion. Observed wetting angles in partially molten peridotite suggest that subcritical crack growth may be important in crack initiation and render viscous deformation insignificant for dikes that are shorter still. Melt is driven into the dike by the difference between the ambient pore pressure and the least compressive stress and driven up the dike by magma buoyancy. The volume increase of the melting reaction, driven by the local drop in pore pressure, may be more important than elastic compressibility of the pore volume and pore fluid in driving melt into the dike. Because channel flow is very efficient relative to porous flow, the dikes are thin, about 6 mm wide when they are a few kilometers tall, for an ambient melt pressure that exceeds the least compressive stress by 1 MPa. This thickness is relatively insensitive to all relevant parameters (including the dike height) because the channel flux increases as the cube of the channel thickness. One implication appears to be that dikes that traverse the lithosphere must drain large segregations of magma, rather than partially molten rock. If dikes feed compliant sills at a depth where the source region is conductively cooled, crystallization onto the dike walls could increase the observable thickness while mass balance maintains a narrow aperture for flow. ¿ 1998 American Geophysical Union