We present a two-dimensional dynamical model for melt extraction from a mantle plume. Mantle material rises at constant velocity Wo until it reaches a depth at which melting begins. The flow in the melt zone above this depth has the form of a stagnation point flow. Melt migrates through the unmelted matrix in response to the total nonhydrostatic pressure gradient, which is the sum of contributions from the deformation of the matrix and the buoyancy of the melt. Melt extraction is modeled as a melt flux through the upper surface of the melt zone. Our main conclusions are as follows: (1) The nonhydrostatic pressure gradient associated with the deformation of the matrix is small relative to the buoyancy of the melt everywhere within the melt zone, and the melt migration within the plume obeys Darcy's law. The rate of melt extraction from a mantle plume is therefore controlled by the buoyancy and viscosity of the melt itself, and not by the viscosity of the matrix. (2) Melt extraction from a plume occurs over an area comparable to that of the plume itself, and about 60-80% of the melt generated within the plume is extracted. Both the geometry and rate of extraction predicted by the model are consistent with observations in the Hawaiian Islands. (3) Layers of segregated melt (magma chambers) are likely to form at the the base of the lithosphere under intraplate volcanoes. ¿American Geophysical Union 1987