Nb3Sn is a prospective material for future superconducting radio frequency (SRF) accelerator cavities. Compared to conventional niobium, the material can achieve higher quality factors, higher temperature operation, and potentially higher accelerating gradients (Eacc ≈ 96 MV/m). In this work, we performed modeling of the Upgraded Injector Test Facility (UITF) at Jefferson Lab utilizing newly constructed Nb3Sn cavities. We studied the effects of the buncher cavity and varied the gun voltage from 200-500 keV. We have calibrated and optimized the SRF cavity gradients and phases for the Nb3Sn five-cell cavities’ energy gains with the framework of the General Particle Tracer (GPT). Our calculations show the beam goes cleanly through the unit. There is full energy gain out of the second SRF cavity but not from the first SRF cavity due to non-relativistic phase shifts.