It has been postulated that the delivery of radiotherapy at ultra-high dose rates ('FLASH') reduces normal tissue toxicities by depleting them of oxygen. The fraction of normal tissue and cancer cells surviving radiotherapy depends on dose and oxygen levels in an exponential manner and even a very small fraction of tissue at low oxygen levels can determine radiotherapy response. To quantify the differential impact of FLASH radiotherapy on normal and tumour tissues, the spatial heterogeneity of oxygenation in tissue should thus be accounted for.The effect of FLASH on radiation-induced normal and tumour tissue cell killing was studied by simulating oxygen diffusion, metabolism, and radiolytic oxygen depletion (ROD) over domains with simulated capillary architectures. To study the impact of heterogeneity, two architectural models were used: (1) randomly distributed capillaries and (2) capillaries forming a regular square lattice array. The resulting oxygen partial pressure distribution histograms were used to simulate normal and tumour tissue cell survival using the linear quadratic model of cell survival, modified to incorporate oxygen-enhancement ratio effects. The ratio ('dose modifying factors') of conventional low-dose-rate dose and FLASH dose at iso-cell survival was computed and compared with empirical iso-toxicity dose ratios.Tumour cell survival was found to be increased by FLASH as compared to conventional radiotherapy, with a 0-1 order of magnitude increase for expected levels of tumour hypoxia, depending on the relative magnitudes of ROD and tissue oxygen metabolism. Interestingly, for the random capillary model, the impact of FLASH on well-oxygenated (normal) tissues was found to be much greater, with an estimated increase in cell survival by up to 10 orders of magnitude, even though reductions in mean tissue partial pressure were modest, less than ∼7 mmHg for the parameter values studied. The dose modifying factor for normal tissues was found to lie in the range 1.2-1.7 for a representative value of normal tissue oxygen metabolic rate, consistent with preclinical iso-toxicity results.The presence of very small nearly hypoxic regions in otherwise well-perfused normal tissues with high mean oxygen levels resulted in a greater proportional sparing of normal tissue than tumour cells during FLASH irradiation, possibly explaining empirical normal tissue sparing and iso-tumour control results.