Flow behavior of polymer solutions through packed beds of particles, which are used as a model of porous media, is experimentally examined. Two packing patterns are prepared and the test fluids used here are aqueous solutions of polyacrylamide (PAA) at three different concentrations. In the measurement of pressure loss, it is observed that the curve of pressure loss makes a sudden change at the critical flow rate. Below the critical flow rate, the pressure loss depends on the shear property of the fluids and can be expressed by the modified Darcy’s law applying the power law model to the shear viscosity of fluids. Beyond the critical flow rate, however, the transient elongational property of the fluids dominates the flow behavior in packed beds of particles and yields the excess pressure loss for the PAA solutions.