Abstract In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drug’s potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs.