In the magnetic application of the bulk high-temperature superconductors, pulsed field magnetization can be applied to practical mobile devices. And as the critical current density of the superconductors increases, the “giant field leaps” or flux jumps that appear during pulsed field magnetization help to magnetize the superconductors by increasing the trapped magnetic field. In this paper, based on the H-formulation, thermal transient equation and Cauchy equation ignoring inertia force, numerical simulations of trapped magnetic field, temperature, and mechanical stresses distributions in the bulk superconductor with reinforcement ring during pulsed field magnetization are presented. During pulsed field magnetization, the effect of mesh size on the trapped field and temperature distribution are considered. In simulation using coarse mesh, thermal spots appear, and “giant field leaps” are accompanied by the emergence of thermal spots. The absolute values of both radial and hoop stresses of the bulk superconductor increase or decrease as the applied field increases or decreases and then increases. At the central point of the superconductor, the maximum value of von Mises stress appears and increases with an increase of the external field, decreases when the external field decreases, and then increases with time.