A large portion of the sediments within the northern Gulf of Mexico contain pore fluid pressures in excess of hydrostatic. Development of geopressure is generally attributed to compaction disequilibrium caused by rapid deposition of low-permeability sediments in the Miocene and Plio-Pleistocene. Numerous studies have examined the formation of overpressures and/or expulsion of geopressured fluids into overlying hydropressured strata. However, very little attention has been given to fluid flow within the geopressured zone itself. Movement of oils from Cretaceous or older source rocks into Plio-Pleistocene reservoirs in the Gulf Basin requires as much as 10 km of vertical migration in a few million years. Precipitation of cements in some geopressured sediments also implies large-scale fluid flow. New evidence from a deep well in the Eugene Island area, offshore Louisiana, indicates that geopressured sediments are mechanically very weak with a Poisson's ratio greater than 0.4 and a shear modulus or rigidity less than 1 GPa. In addition, large-scale fluid flow either through interconnected pores or fractures is not occurring in this location, at least at present. An alternative hypothesis is that upward fluid transport in geopressured sediments is caused by buoyancy-driven propagation of isolated fluid-filled fractures. Using linear fracture mechanics, I show that vertical fractures with lengths of a few meters can propagate at velocities of 1000 m/yr. Mass flux rates (~100 kg/m2/yr) are significant assuming a mechanism for formation of fluid-filled fractures exists, such as hydrofracturing when fluid pressures exceeded the minimum confining stress. Fracture propagation velocity and mass flux rate are strongly dependent on the shear modulus of geopressured sediments. ¿ American Geophysical Union 1996