This paper examines Hall Effect measurements of stainless steel 316 (SS316) under applied stress. In free carrier gas model, the Hall coefficient is inverse proportional to charge carrier density, and thus expected to vary under stress. This relationship is simpler than that of the electrical conductivity, which depends not only on carrier density but also on the mean-free path. Thanks to the simpler underlying physics, it is anticipated that Hall Effect measurements can show more straightforward stress dependency than the conductivity-based measurements such as eddy current. In contrast, at least in the free carrier approximation with single type of carriers, the Hall coefficient has no dependence on the mean free path, while depending on elastic stress. We measured the Hall coefficient of SS316, in comparison with that of copper. First, the expected stress dependence of the Hall coefficient due to the simple volume effect under the stress was estimated in free carrier gas model. Second, Hall coefficients of these metals were measured under varying magnetic fields. It was observed that SS316 exhibited magnetic field dependency of the Hall coefficient outside measurement errors, while no such dependence was observed for copper. Third, the relationship between tensile stress and the Hall coefficient in SS316 was measured. The Hall coefficient increases in magnitude linearly under tension. The stress sensitivity is higher than predicted from the simple volume effect.