Several workers have reported on the observation of a peak, in the magnetic flux trapped by polycrystalline type II superconductors, when plotted versus the cooling fields from T-C, and versus the magnitude of the half-cycle fields applied after zero-field cooling. We report on our observations of this behavior in a niobium sample and present a detailed model which accounts for these observations. The crucial feature of the model is that it takes into account the effect of the return magnetic field of the magnetized grains on the macroscopic continuous intergranular persistent critical currents induced to circulate in the specimen by the externally applied magnetic field. Our analysis indicates that attempts to trap magnetic fields, greater than the calculated peaks, inside hollow and solid cylinders can lead to significantly diminished results. Our analysis may also apply in calculations of hysteresis losses in type II superconducting cables.