Laser shock peening (LSP) is a surface modification technique to improve the mechanical properties of metals and alloys, where physical phenomena are difficult to investigate, due to short time scales and extreme physical values. In this regard, simulations can significantly contribute to understand the underlying physics. In this paper, a coupled simulation approach for LSP is presented. A global model of laser–matter–plasma interaction is applied to determine the plasma pressure, which is used as surface loading in finite element (FE) simulations in order to predict residual stress (RS) profiles in the target material. The coupled model is applied to the LSP of AA2198-T3 with water confinement, 3 × 3 mm² square focus and 20 ns laser pulse duration. This investigation considers the variation in laser pulse energy (3 J and 5 J) and different protective coatings (none, aluminum and steel foil). A sensitivity analysis is conducted to evaluate the impact of parameter inaccuracies of the global model on the resulting RS. Adjustment of the global model to different laser pulse energies and coating materials allows us to compute the temporal pressure distributions to predict RS with FE simulations, which are in good agreement with the measurements.