Laser shock peening (LSP) is an advanced surface strengthening technology that uses laser shock waves (LSWs) to induce severe plastic deformation, considerable compressive residual stress, and grain refinement, and thereby improve the fatigue performance of metallic materials. Understanding the spatiotemporal distribution of the stress wave is important for precisely managing the strengthening effect of LSP. In this paper, the stress distribution of LSWs and the equation for LSW-induced residual strain in visco-elasto-plastic materials are presented. The formation of LSW-induced micro dimples on the surface is noteworthy. We derived an approximate equation for the maximum micro-dimple depth induced by LSWs. Finally, we measured the micro-dimple depths induced by LSWs at different peak pressures and verified the reliability of the theoretical calculation by comparing the calculated data with the experimental data. The micro-dimple depth can serve as an indicator of the effectiveness of LSP and improvement in fatigue performance. This characteristic can be utilized as a non-destructive testing method. This study has demonstrated the potential for promoting and applying of LSP in different industries.