Laser peen forming (LPF) is an appealing technique for forming metal sheets using high-energy, short-duration laser pulses. The deformation of the target metal plate is closely related to the magnitude and distribution of laser-induced residual stress. Consequently, the relationship between process parameters and residual stress is worth researching. In this research, two process parameters in LPF, laser energy and coverage ratio (spot distance essentially), and one workpiece parameter, plate thickness, were examined through an element method (FEM) of multiple square-spot laser shock peening (SSLSP). Corresponding experiments of SSLSP on aluminum alloy 2024-T351 test blocks were conducted, together with an X-ray diffraction (XRD) residual stress measurement and a surface morphology observation. The FEM simulation and experimental results show that congested laser spots had a significant influence on the magnitude of compressive residual stress; higher laser energy was beneficial to the depth of the compressive stress layer but could decrease its magnitude. Therefore, for better forming ability, higher laser energy and a higher coverage ratio are beneficial; for surface strengthening, laser energy should not be too large, and the coverage ratio should be larger than 100% to ensure that the residual stress on the treated surface is compressive, resulting in better surface integrity.