In vivo tumours are highly heterogeneous, often comprising regions of hypoxia and necrosis. Radiotherapy significantly alters the intratumoural composition. Moreover, radiation-induced cell death may occur via a number of different mechanisms that act over different timescales. Dead material may therefore occupy a significant portion of the tumour volume for some time after irradiation and may affect the subsequent tumour dynamics. We present a three phase tumour growth model that accounts for the effects of radiotherapy and use it to investigate how dead material within the tumour may affect the spatio-temporal tumour response dynamics. We use numerical simulation of the model equations to characterise qualitatively different tumour volume dynamics in response to fractionated radiotherapy. We demonstrate examples, and associated parameter values, for which the properties of the dead material significantly alter the observed tumour volume dynamics throughout treatment. These simulations suggest that for some cases it may not be possible to accurately predict radiotherapy response from pre-treatment, gross tumour volume measurements without consideration of the dead material within the tumour.