Additive manufacturing (AM) of metals is increasingly used in engineering applications; however, the anisotropy of mechanical properties caused by the layer-by-layer deposition process poses challenges for constitutive modelling. This study focuses on 316L stainless steel produced by Wire Laser Metal Deposition (WLMD) and aims to develop a Johnson–Cook (J–C) constitutive model suitable for numerical simulations of this material. Tensile tests were performed on specimens printed in four build orientations (0°, 45°, 90°, and cross-directional XX), and the engineering stress–strain curves were converted into true stress–strain data. Young’s modulus, yield strength (Re₀.₂), ultimate tensile strength (UTS), and strain at UTS were determined for each orientation. The results demonstrated pronounced anisotropy: UTS ranged from ~610 MPa (90°) to ~660 MPa (0°), while total elongation varied between 28% and 37%, depending on the build direction. Based on the true stress–strain data, simplified J–C parameters (A, B, n) were identified for each orientation, achieving a high quality of fit (R² > 0.97). The findings confirm that build orientation significantly influences the mechanical response of WLMD-processed 316L, and that direction-dependent J–C parameters are necessary for reliable finite element (FE) simulations. The proposed model provides a foundation for more advanced constitutive descriptions, including strain-rate and temperature effects.