Laser Shock Peening (LSP) turned out to be the most efficient surface engineering process for advanced materials to induce beneficial deep compressive residual stress which helps in improving mechanical, fatigue properties and surface damage resistance. But, analyzing the nonuniform distribution of residual stresses in the treated sample with X-ray diffraction (XRD) is much time taking and a costly process. This problem can be resolved with LSP finite element numerical simulation model which is feasible with the realistic experimental process. The FE model allows the user to control the laser parameters in order to achieve the optimal level of all controllable parameters. This study is intended to analyze and optimize the influence of laser processing parameters that assists in inducing the residual compressive stress with minimal surface deformation. A Ti6Al4V material model with Johnson-Cook's visco-elastic-plastic material behavior law is prepared for LSP simulation. Gaussian pressure profile is utilized for uniform loading of the targeted zone for the proposed model. Taguchi Grey Relational Analysis (TGRA) with L27 orthogonal array is applied to LSP simulation, and the results were analyzed with consideration of multiple response measures. It is noted that surface deformation is increased with the rise in a number of laser shots and pressure pulse duration. Maximum compressive residual stresses are falling for higher levels of laser spot diameter, laser spot overlap and laser power density. The correlation is observed between the FE simulation and the published results. The optimal set of process parameters are obtained for improving the LSP on Ti alloys. © 2020 World Scientific Publishing Company.