Conventional assessments of the mechanical properties of polycrystalline high RRR niobium via tensile testing have revealed unusually low apparent Young’s moduli and yield strength in annealed samples. These observations motivated the current investigation of a variety of possible contributors: crystallographic texture, grain size, and impurity concentration. It is shown that the crystallographic textures of a single lot of niobium are essentially unchanged by post‐recrystallization anneals at temperatures up to 800°C. Ultrasonic measurements reveal that the elastic response is not degraded by annealing. Rather, the material’s extremely low yield point gives the impression of a low elastic modulus during tensile testing.