Bulk high-temperature superconductors are widely used in various superconducting devices for their high critical current density and the ability to trap large magnetic field. In some applications, bulk superconductors can be arranged in an array structure to increase the magnetic field strength. However, rectangular bulk superconductors can be arranged more compactly than commonly used cylindrical bulk superconductors. The unique shape of rectangular bulk superconductors results in different distributions of electromagnetic fields, temperature, and stress under a pulsed-field magnetization (PFM) than for cylindrical bulk superconductors. In bulk superconductors, growth sector boundaries and growth sector regions have different critical current density, resulting in an uneven critical current density. Therefore, in this study, the electromagnetic and mechanical behavior of non-uniform rectangular bulk superconductors during the PFM process is investigated. The corresponding distribution and variation in the magnetic field, current, temperature, and stress in the bulk are calculated and analyzed. The influence of rectangle aspect ratio on the electromagnetic and mechanical behavior is discussed. The calculation results show that the magnetic flux jumps occur accompanied by sudden changes in the temperature and pressure. The effect of the aspect ratio of rectangular bulk superconductors on their electromagnetic and mechanical properties is analyzed. The influence of preexisting cracks in a non-uniform rectangular bulk superconductor on the simulation results is discussed. The numerical results indicate that the presence of an edge crack exacerbates the magnetic flux jump as well as the jumps in the temperature and stress. However, a central crack has a relatively small effect on the stability of a bulk superconductor.