In this paper we report an investigation of the unsteady-state flow of polymer solutions through granular porous media. The experiments were performed using high-molecular-weight nonionic and anionic polyacrylamides dissolved in water containing NaCl and model porous media obtained by packing silicon carbide (SiC) grains having a narrow grain size distribution. Before injection in porous media, the polymer solutions were carefully filtered according to a method that was proved to be efficient in removing any possibly remaining microgels, The SIC grain surface was passively oxidized by a controlled thermal treatment in order to obtain a surface partially covered by a thin silica layer having adsorption properties similar to those of quartzitic sand. By packing SiC grains of different sizes, porous media having identical adsorption properties and well-known pore throats sizes can be obtained with a good reproducibility. Parameters investigated include pore size, velocity gradient, polymer concentration, and adsorption energy. A striking unsteady-state flow behavior (pressure build-up at constant Row rate) is observed when three conditions are fulfilled: (a) the velocity gradient is larger than that known to be able to induce a coil-stretch transition, (b) the polymer adsorbs on the pore surfaces, and (c) the length of stretched macromolecules is larger than the effective pore throat diameter. When one of these conditions is not satisfied the Row remains steady. These observations are interpreted by a mechanism involving the adsorption and bridging across pore restrictions of elongated chains. We propose to refer to this peculiar mode of polymer adsorption as bridging adsorption,