Woven structures are steadily emerging as excellent reinforcing components in composite materials. Metallic woven meshes, unlike most woven fabrics, show high potential for strengthening via classical methods such as heat treatment. Development of strengthening processes for metallic woven materials, however, must account not only for behavior of the constituent wires, but also for the interactions between contacting wires. Yield behavior of a 325 × 2300 stainless steel 316L (SS316L) twill dutch woven wire mesh is analyzed via experimental data and 3D numerical modeling. The effects of short dwell-time heat treatment on the mechanical properties of this class of materials is investigated via uniaxial tensile tests in the main weave orientations. Scanning electron microscopy (SEM) is employed to investigate the effects of heat treatment on contacting wire interaction, prompted by observations of reduced ductility in the macrostructure of the mesh. Finally, the finite element method (FEM) is used to simulate the accumulation of plastic deformation in the mesostructure of the mesh, investigating how this wire level plasticity ultimately affects global material yielding.