Migration of hydrocarbons deals with the subsequent movement of petroleum after expulsion from the source rock through water saturated reservoirs or through permeability created by fractures and faults. Although the underlying principles that control the fluid movement in porous media (reservoirs) are well understood by reservoir engineers, less is known about the flow characteristics in low-permeable, porous media, such as clays and shales. For flow considerations, the primary parameters are porosity, permeability and the fluid potential gradients. For clays and shales, these parameters are poorly known; yet these control the time periods during which fluid flow occurs in sedimentary basins (100 years to 100 million years). In this paper, I examine the parametric dependence of the time constantsof fluid flow in low permeability sediments on its porosity and permeability. This is accomplished in two parts. In the first part, a technique is presented to investigate the effect of fluid flow in shales which causes undercompaction and buildup of fluid pressures in excess of normal hydrostatic pressure. The technique is pre-drill in nature; it uses seismic velocity analysis of common depth point gather of surface seismic data and is based on the concept developed by Hottmann and Johnson (1965) and Pennebaker (1968). In the second part of the paper, the flow characteristics are discussed in the basin scale. I develop a model that describes the fluid flow in a continuously accreting and subsiding clastics basins, such as the Gulf of Mexico. I examine the pressure characteristics of such a basin by digital simulations and study the effect of the permeability variation of shales on the geologic time dependence of the fluid flux in the sediments, the basin subsidence rate and the pressure buildup with depth. The model incorporates both mechanical compaction and burial diagenesis involving smectite to illite conversion of shales. The latter is based on a kinetic theory of chemical reaction in which the time-temperature history is provided by the solution of an appropriate heat conduction equation. This model of geopressure has a practical application since it deals with the generation and maintenance of abnormally high fluid pressures over geologic time and impacts the hydrocarbon migration in clastic basins.