Mid-ocean ridge volcanism is largely concentrated within a few kilometers of the spreading axis. Geophysical models of upwelling induced melting beneath a ridge axis predict significant melting within a ~100 kilometer wide regin beneath a ridge axis. This provides a strong constraint for testing models of melt migration beneath a spreading center since a successful melt migration mechanism must be able to focus melt from a broad region of melt production to the narrow emplacement zone at the ridge axis. Tensile dike propagation transport of melt within the mantle would move melt away from the ridge axis and thus does not satisfy this constraint. However, porous flow of melt within a viscosity deformation asthenosphere is a visible possibility. Models of porous flow are constructed which consider the effects of mantle flow-induced pressure gradients and strain-induced anisotropic permeability on porous melt migration. In order for flow-induced pressure gradients to shape melt migration the sub-ridge asthenospheric viscosity must be 1021 Pa-s, two orders of magnitude larger than currently accepted values. Mantle strain-induced anisotropic permeability variations can explain the focusing of melt towards the ridge axis of the ratio of the directional anisotropic permeabilities is as small as 3. Furthermore, mantle strain-induced anisotropy in rock permeability may be an important mechanism shaping melt migration within the mantle. ¿ American Geophysical Union 1987