This study examines the microstructure, crystallographic texture evolution, and mechanical properties of stainless steel 316L fabricated through electron beam melting using a stochastic scan strategy at a preheat temperature of 1123 K. X-ray diffraction confirmed the presence of a pure austenitic phase in the fabricated material. Equiaxed cellular structures were observed in the center of the melt pool regions and elongated cellular structures observed at the melt pool overlap regions. A finite element-based numerical model was employed to estimate the thermal gradients and solidification rates within the melt pool of an electron beam spot. Microstructural analysis indicated a generation of columnar grains from the bottom to the top of the build owing to high thermal gradients. A crystallographic texture investigation showed a generation of strong fiber texture along the build direction of the material and reported that the stress distributions within the melt pool led to a strong crystallographic texture driven by the stress evolution observed from thermokinetic computational modelling of the electron beam-melting process. Mechanical properties were assessed using profilometry-based indentation plastometry, demonstrating strain hardening at a high temperature of 773 K.