Laser shock peening is an advanced surface treatment technology that can significantly improve the performance of metallic components. To study the residual stress distribution and the propagation law of the dynamic stress in a round rod structure after laser shock peening, a laser shock peening finite element model was established for aluminum alloy round rod fatigue test samples. The residual stress distribution of the sample after laser shock peening with different spot sizes was analyzed in three directions. The propagation law of the dynamic stress was analyzed by a simulation of the dynamic stress change process. The accuracy of the model was experimentally verified. The results showed that as the spot size increased, the range of surface residual stress gradually increased in the axial direction. The degree of residual stress range increase in the circumference direction was smaller than the increase in the axial direction. The convergence of the unloaded tensile stress wave and the reflected tensile stress wave led to the formation of tensile residual stress in the round rod center. The compressive stress generated at the impact edge increased the final compressive residual stress. As the spot size decreased, the fatigue life of the samples increased. These conclusions can not only guide the selection of process parameters for a curved surface structure but also provide a reference for the analysis of the laser-induced shock wave propagation mechanism for specific structures.