Elastic mechanical properties of 316 L stainless steel samples fabricated using laser powder bed fusion were studied non-destructively through resonant ultrasound spectroscopy. Samples in five different conditions were obtained by varying the laser power from 103 W (the highest density condition) to 68 W (the lowest density condition) at constant laser speed, producing samples with a volume energy density in the 24.5–16.5 J/mm3 range and volumetric porosity in the 0.1–10% range. The observed elastic mechanical properties are discussed taking into consideration the bulk texture developed and quantitative pore characteristics studied using high-energy high-resolution synchrotron X-ray diffraction and X-ray computed micro-tomography, respectively. Furthermore, empirical exponential relationships are provided to express the functional dependence of Young's and shear moduli with porosity.