The transport critical current J c in a polycrystalline superconductor is a hysteretic function of applied magnetic field H 0 due to flux trapping by grains. This effect has been observed by several groups and attempts have been made to calculate the intergranular field H i as a function of the applied H 0 in terms of an effective geometrical demagnetization factor D. In general a first-principles calculation of D is very difficult, and furthermore, D is not constant but is itself a hysteretic function of H 0. We develop a self-consistent scheme to extract the D and H i directly from the J c (H 0) data itself. Our model exploits the fact that there are two field ranges for which the demagnetizing field is a simple function of H 0. At low virgin fields, in the Meissner state, the susceptibility v ϷϪ1/4 is well defined, leading to a multiplicative correction: H i ϭH 0 /(1 ϩD4 v). For fields that have returned from high values, a complete critical state is established and M is well defined-although v is unknown. This leads to an additive correction: H i ϭH 0 ϪD4M for the total field. By matching J c data in increasing and decreasing fields that satisfy these special cases, it is possible to extract the relevant parameters of the problem without detailed knowledge of the demagnetization geometry. We use this model to analyze data measured on sintered YBa 2 Cu 3 O 7 superconductive rods.