Abundant cross-cutting dikes have been observed in mantle periodtities. These dikes are inferred to have formed while the material was a mostly crystalline mush beneath a ridge axis. The presence of these dikes indicates that the mush was able to fracture. The physics of the growth of vein and dikes and the extent to which they tap melt are investigated in this paper. Once small veins are initiated, they tend to open if the fluid pressure within them exceeds the least principal stress. Porous flow into the veins is necessary for them to open. This implies a melt pressure gradient and that the melt pressure in growing veins is less than the regional pressure. The opening rate and pore pressure decrease are obtained considering both porous flow and viscous deformation around the vein. The stress concentration factor driving vein lengthening is largest for veins near the compaction length. If the critical stress concentration factor is sufficiently low, vein growth and tapping of the veins by dikes reduces the melt pressure to near the least principal stress. Then the matrix of a material undergoing deviatoric strain is compacted because the melt pressure is less the ''pressure'' of the solid. Retention of significant melt directly beneath the axes of fast ridges is expected because the deviatoric strains are low there. However, computed contours of melt fraction are weakly dependent on the efficacy of tapping of melt by dikes. Numerical models indicate that about half of the melt is tapped by dikes if the shape of the conduit is thermally controlled. Tapping of melt by density-driven porous flow is enhanced if the melt viscosity is low owing to high temperatures. This process, rather than dikes, was probably important in the Archean and is now important beneath hotspot ridges, such as Iceland. Shear strain rates in the asthenosphere are long enough that significant quantities of melt should be extracted if partial melt exists in intraconnected pores and the critical stress concentration factor for vein growth is exceeded.