Core velocity measurements are an essential part of any 4D seismic feasibility study. During recently conducted core velocity measurements, we found some interesting results regarding velocity anisotropy and hysteresis. These findings include: (1) the stress sensitivity of velocity varies depending on the propagation direction, (2) velocities measured during loading have a significantly larger stress sensitivity than those measured during unloading, and (3) horizontal effective stress has a noticeable impact on velocity anisotropy. We conducted rock physics analysis and 1D seismic forward modeling, incorporating velocity anisotropy, and found that the estimated 4D seismic signal is largely affected by velocity anisotropy and hysteresis. These findings suggest the importance of considering the velocity measurement direction and the nature of the stress change to obtain a realistic 4D seismic signal. Neglecting these considerations may lead to a significantly underestimated or overestimated modeled seismic response.