Laser shock peening (LSP) is a method of work hardening used to improve fatigue life. Finite element (FE) modeling of LSP lacks confidence, primarily due to the unknown shape of the acting pressure impulse in both time and space. This work developed and tested an integrated FEM/optimization model to determine a 'best fit' pressure impulse shape based on easy to measure surface displacement and residual stress data from a single LSP burst. Isight optimization software was used in conjunction with Abaqus FEM, MATLAB, and Excel to utilize the Hooke-Jeeves optimization algorithm for datamatching. Favorable algorithm parameters were determined for a discretized optimization space then applied to the continuous optimization space to match FEM generated target data. Residual stress results matched to within 4.5% maximum difference, and surface displacement results matched to within 2.5% maximum difference. This modeling tool shows great potential for use in matching test data from LSP treated specimens, resulting in improved FEM confidence for engineering design application.