The transport critical current density Jc has been measured in high quality polycrystalline YBa2Cu3O7 samples made from extruded preforms. The hysteretic response of Jc to applied magnetic fields was studied as a function of temperature (77–87 K) and sample morphology for various field sweeps in the 0–5 KOe range. A variety of samples show a basic Jc ∼ H−n behavior where n depends on temperature, but is independent of the other variables. A simple model of the local magnetic field distribution is presented and compared to the data, and the theoretical implications of the power law behavior are considered.