Results of a series of two-dimensional numerical experiments of mantle flow, melting, and melt migration under a spreading center are reported. The model predicts the distribution of melt in the subridge mantle, the width over which most melt is delivered to the crust, and the thickness of crust. The sources of buoyancy considered are thermal expansion, compositional variation caused by melt extraction, and the phase change of solid to melt. We infer that the steady state average viscosity of the mantle below a ridge cannot be much less than about 1019 Pa s. For a lower average viscosity, thermal convection causes rapid cooling of a large region under a ridge, raising the viscosity. Results imply that transient increases in mantle temperature should lead to larger increases in the oceanic crustal thickness for slow spreading ridges than for fast spreading ridges. We assume that the viscosity is proportional to exp (-ϕ/ϕ0), where ϕ is melt fraction. We parameterize the permeability in terms of the reference velocity for percolation of the melt &ngr;r, where the relative velocity of melt to solid is &ngr;rϕ. Analytic approximations are used to extrapolate the model results to large values of permeability and small values of ϕ0. If &ngr;r is less than 1 m/yr, then more melt would be retained in the subridge mantle than is estimated from analysis of topography and gravity data at fast spreading centers. For &ngr;r greater than about 100 m/yr, so little melt would be retained in the mantle that it is difficult to explain the gravity data and the low shear wave velocity structure close to the East Pacific Rise estimated from seismic surface waves. Buoyancy effects can lead to a region of mantle upwelling and melting that is as narrow as the observed zone of oceanic crustal accretion. For most melt to be added to the crust within a few kilometers of a fast spreading center requires that ϕ0 be less than 0.015 if &ngr;r equals 1 m/yr and less than 0.003 if &ngr;r is 100 m/yr. ¿ American Geophysical Union 1993