Recent measurement from Ocean Drilling Program leg 110 and Deep Sea Drilling Project leg 78a indicate that pore pressures near the toe of the Barbados accretionary prism may be close to lithostatic and that the d¿collement is a zone with relatively high rates of fluid flow and methane transport. We used a numerical model of fluid flow to estimate intrinsic permeabilities, pore pressures, and flow velocities that are consistent with these observations. Model results suggest that the permeability of the d¿collement may be 3--5 orders of magnitude greater than that of adjacent prism sediments. If permeabilities in the prism vary with depth in a manner similar to those in sedimentary basins, the average intrinsic permeability of the d¿collement, kd, must be about 10-14 m2. When kd is 10-13 m2, high pore pressures do not develop near the deformation front in the model. If kd is 10-15 m2, simulated pressures are unrealistically high in both the prism and underthrust sediments arcward of the deformation front. Water originating from compaction in the d¿collement and underthrust sediments flows laterally seaward, while water expelled from prism sediments flows upward to the ocean floor. However, flow velocities are small, and the net motion of pore water in prism and underthrust sediments is arcward relative to the deformation front because of tectonic transport. Pore water migrates seaward in spite of tectonic transport only in descrete zones with higher permeability, in this case the d¿collement. ¿American Geophysical Union 1990