After a single dose of radiation, transient changes caused by cell death are likely to occur in the oxygenation of surviving cells. Since cell radiosensitivity increases with oxygen concentration, reoxygenation is expected to increase the sensitivity of the cell population to a successive irradiation. In previous papers we proposed a model of the response to treatment of tumour cords (cylindrical arrangements of tumour cells growing around a blood vessel of the tumour). The model included the motion of cells and oxygen diffusion and consumption. By assuming parallel and regularly spaced tumour vessels, as in the Krogh model of microcirculation, we extend our previous model to account for the action of irradiation and the damage repair process, and we study the time course of the oxygenation and the cellular response. By means of simulations of the response to a dose split in two equal fractions, we investigate the dependence of tumour response on the time interval between the fractions and on the main parameters of the system. The influence of reoxygenation on a therapeutic index that compares the effect of a split dose on the tumour and on the normal tissue is also investigated.