PURPOSE: To develop a theoretical model for oxygen delivery to tumors, and to use the model to simulate the effects of changing the affinity of hemoglobin for oxygen on tumor oxygenation. METHODS AND MATERIALS: Hemoglobin affinity is expressed in terms of P(50), the partial pressure of oxygen (Po(2)) at half saturation. Effects of changing P(50) on arterial Po(2) are predicted using an effective vessel approach to describe diffusive oxygen transport in the lungs, assuming fixed systemic oxygen demand and fixed blood flow rate. The decline in oxygen content of blood as it flows through normal tissue before entering the tumor region is assumed fixed. The hypoxic fraction of the tumor region is predicted using a three-dimensional simulation of diffusion from a network of vessels whose geometry is derived from observations of tumor microvasculature in the rat. RESULTS: In air-breathing rats, predicted hypoxic fraction decreases with moderate increases in P(50), but increases with further increases of P(50), in agreement with previous experimental results. In rats breathing hyperoxic gases, and in humans breathing either normoxic or hyperoxic gases, increased P(50) is predicted to improve tumor oxygenation. CONCLUSIONS: The results support the administration of synthetic agents to increase P(50) during radiation treatment of tumors.