A pulsed neutron spallation target is subjected to very short but intense loads from repeated proton pulses. Approximately 60% of the energy from each proton pulse is deposited into the mercury target material and the stainless-steel target structure, leading to a high-pressure region in both the stationary target structure and the flowing mercury. The high-pressure region propagates and leads to fluid-structure interaction. The resultant loading on the target structure containing liquid mercury is difficult to predict, although various simulation approaches and material models for the mercury have been tried. To date, the best match of simulation to experimental data is obtained by using an equation of state (EOS) material model with a specified tensile cutoff pressure, which simulates the cavitation threshold. The inclusion of a threshold to represent cavitation is key to the successful predictions of stress waves triggered by the high-energy pulse striking the mercury and vessel. However, recent measurements of target structure strain show that significant discrepancies remain between the measured and simulated strain values in the EOS mercury model. These differences grow when noncondensable helium gas is intentionally injected into the flowing mercury to reduce the loading on the structure. An EOS-based proportional–integral–derivative (PID) mercury model has been proposed to reduce the gap between the measured and simulated vessel strain responses for targets with gas injection. The conceptual and numerical description and initial investigation of the PID model are presented in previous work. Further studies of this PID model — including the sensitivity of the structure’s strain response to model parameters (the tensile cutoff, PID parameters Kp, Ki, and Kd) — are reported in this article. Results show the strain response is more sensitive to changes in the tensile cutoff value than to changes in the model parameters Kp, Ki, and Kd. These results will aid in future work where the model parameters will be optimized to match simulation data to strain measurements.