This work studies the use of laser shock peening (LSP) to improve back stress in additively manufactured (AM) 316L parts. Unusual hardening behavior in AM metal due to tortuous microstructure and strong texture poses additional design challenges. Anisotropic mechanical behavior complicates application for mechanical design because 3D printed parts will behave differently than traditionally manufactured parts under the same loading conditions. The prevalence of back-stress hardening or the Bauschinger effect causes reduced fatigue life under random loading and dissipates beneficial compressive residual stresses that prevent crack propagation. LSP is known to improve fatigue life by inducing compressive residual stress and has been applied with promising results to AM metal parts. It is here demonstrated that LSP may also be used as a tool for mitigating tensile back-stress hardening in AM parts, thereby reducing anisotropic hardening behavior and improving design use. It is also shown that the method of application of LSP to additively manufactured parts is key for achieving effective back-stress reduction. Back stress is extracted from additively manufactured dog bone samples built in both XY and XZ directions using hysteresis tensile. Both LSPed and as-built conditions are tested and compared, showing that LSPed samples exhibit a significant reduction to back stress when the laser processing is applied to the sample along the build direction. Electron backscatter diffraction (EBSD) performed under these conditions elucidates how grain morphologies and texture contribute to the observed improvement. Crystal plasticity finite element (CPFE) modeling develops insights as to the mechanisms by which this reduction is achieved in comparison with EBSD results. In particular, the difference in plastic behavior across build orientations of identified crystal planes and grain families are shown to impact the degree of LSP-induced back-stress reduction that is sustained through tensile loading.