We previously developed a three-dimensional computational model of oxygen transport in the renal medulla. In the present study, we employed this model to quantify the sensitivity of renal medullary oxygenation to four of its major known determinants: medullary blood flow (MBF), medullary oxygen consumption rate (VO2,M), hemoglobin concentration in the blood (Hb), and renal perfusion pressure (RPP). We also examined medullary oxygenation under special conditions of hydropenia, extracellular fluid volume expansion by infusion of isotonic saline, and hemodilution during cardiopulmonary bypass (CPB). Under baseline (normal) conditions, the average medullary tissue PO2 predicted for the whole renal medulla was ~30 mmHg. The periphery of the interbundle region in the outer medulla (OM) was identified as the most hypoxic region in the renal medulla, which demonstrates that the model prediction is qualitatively accurate. Medullary oxygenation was most sensitive to changes in RPP followed by Hb, MBF and VO2,M, in that order. The medullary oxygenation also became sensitized by pro-hypoxic changes in other parameters, leading to a greater fall in the medullary tissue PO2 when multiple parameters changed simultaneously. Hydropenia did not induce a significant change in medullary oxygenation compared to the baseline state, while volume expansion resulted in a large increase in the inner medulla (IM) tissue PO2 (by ~15 mmHg). Under conditions of CPB, the renal medulla became severely hypoxic, due to hemodilution, with one-third of the OSOM tissue having a PO2 of less than 5 mmHg.