Using uniaxial tensile and hardness testing, we evaluated the variability and anisotropy of the mechanical properties of an austenitic stainless steel, UNS S17400, manufactured by an additive process, selective laser melting. Like wrought materials, the mechanical properties depend on the orientation introduced by the processing. The recommended stress-relief heat treatment increases the tensile strength, reduces the yield strength, and decreases the extent of the discontinuous yielding. The mechanical properties, assessed by hardness, are very uniform across the build plate, but the stress-relief heat treatment introduced a small non-uniformity that had no correlation to position on the build plate. Analysis of the mechanical property behavior resulted in four conclusions. (1) The within-build and build-to-build tensile properties of the UNS S17400 stainless steel are less repeatable than mature engineering structural alloys, but similar to other structural alloys made by additive manufacturing. (2) The anisotropy of the mechanical properties of the UNS S17400 material of this study is larger than that of mature structural alloys, but is similar to other structural alloys made by additive manufacturing. (3) The tensile mechanical properties of the UNS S17400 material fabricated by selective laser melting are very different from those of wrought, heat-treated 17-4PH stainless steel. (4) The large discontinuous yielding strain in all tests resulted from the formation and propagation of Lüders bands.