Although chemotherapy has revolutionized the treatment of haematological tumours, in many common solid tumours the success has been limited. Some of the reasons for the limitations are: the timing of drug delivery, resistance to the drug, repopulation between cycles of chemotherapy and the lack of complete understanding of the pharmacokinetics and pharmacodynamics of a specific agent. Cisplatin is among the most effective cytotoxic agents used in head and neck cancer treatments. When modelling cisplatin as a single agent, the properties of cisplatin only have to be taken into account, reducing the number of assumptions that are considered in the generalized chemotherapy models. The aim of the present paper is to model the biological effect of cisplatin and to simulate the consequence of cisplatin resistance on tumour control. The 'treated' tumour is a squamous cell carcinoma of the head and neck, previously grown by computer-based Monte Carlo techniques. The model maintained the biological constitution of a tumour through the generation of stem cells, proliferating cells and non-proliferating cells. Cell kinetic parameters (mean cell cycle time, cell loss factor, thymidine labelling index) were also consistent with the literature. A sensitivity study on the contribution of various mechanisms leading to drug resistance is undertaken. To quantify the extent of drug resistance, the cisplatin resistance factor (CRF) is defined as the ratio between the number of surviving cells of the resistant population and the number of surviving cells of the sensitive population, determined after the same treatment time. It is shown that there is a supra-linear dependence of CRF on the percentage of cisplatin-DNA adducts formed, and a sigmoid-like dependence between CRF and the percentage of cells killed in resistant tumours. Drug resistance is shown to be a cumulative process which eventually can overcome tumour regression leading to treatment failure.