Detrimental subsurface tensile residual stresses occur in laser powder bed fusion (LPBF) due to significant temperature gradients during the process. Besides heat treatments, laser shock peening (LSP) is a promising technology for tailoring residual stress profiles of additively manufactured components. A multi step process simulation is applied aiming at predicting the residual stress state after applying LSP to a cuboid shaped specimen manufactured by LPBF in two different building directions as well as comparing it with a post-build heat treatment. The validity of the numerical simulation is evaluated based on comparisons of residual stresses determined by incremental hole drilling technique within different stages of the multi step process: in the as-build condition, after subsequent heat treatment as well as after applying LSP to the as-build and heat treated specimens, showing overall a good experimental-numerical agreement throughout each of the process stages. Applying a heat treatment to the as-build LPBF sample at 700°C for 6h showed not to be effective in eliminating the surface tensile stress entirely, reducing the tensile residual stresses by 40%. However, the application of LSP on LPBF components showed promising results: LSP was able even to convert the detrimental near surface tensile residual stresses in the LPBF component into compressive residual stresses next to the surface, which is known to be beneficial for the fatigue performance.