In the presented study, LPBF 316L stainless steel tensile specimens were manufactured in three different orientations for the analysis of anisotropy. The first set of specimens was built vertically on the build platform, and two other sets were oriented horizontally perpendicular to each other. Tensile test results show that mean Young’s modulus of vertically built specimens is significantly less then horizontal ones (158.7 GPa versus 198 GPa), as well as yield strength and elongation. A role of residual stress in a deviation of tensile loading diagrams is investigated as a possible explanation. Simulation of the build process on the basis of ABAQUS FEA software was used to predict residual stress in 316L cylindrical specimens. Virtual tensile test results show that residual stress affects the initial stage of the loading curve with a tendency to reduce apparent Young’s modulus, measured according to standard mechanical test methods.