We describe a mathematical model of cell growth and death and explain how it can be used to integrate data from classic tissue culture experiments on antitumour agents and thus aid the identification of their mechanism of action. Experimental data relating to time- and dose-dependent changes in growth rate, cell cycle distribution, plus apoptotic and senescent fractions, are reinterpreted in terms of modulations to kinetic parameters that describe the rates at which cells transit between phenotypic compartments. The mathematical model is analytical, in the sense that the kinetic parameters are calculated from the experimental data directly, without any fitting process. Since the kinetic parameters are much more directly related to potential molecular targets than are the experimentally measured quantities, this approach can provide a more informative picture of the mechanism of action of the antitumour agent under investigation. We demonstrate the potential value of our model by applying it to data from RHPS4 (3,11-difluoro-6,8,13-trimethyl-8H-quino [4,3,2-kl] acridinium methosulfate). This agent is a DNA-interactive pentacyclic acridine for which at least three potential mechanisms of antitumour activity have been identified. Firstly RHPS4 is a telomerase inhibitor, secondly it is a telomerase-independent destabiliser of telomeres, and thirdly it is a telomere-independent binder to genomic DNA. Each mechanism can induce a separate, but overlapping, pattern of cellular responses, making the interpretation of tissue culture data very complex. Here we study the time- and dose-dependent effects of RHPS4 on the HCT116 cell line, and develop a five-compartment mathematical model to interpret the data. Application of the model to the data suggests that RHPS4 increases the rate at which cells became senescent state but, rather surprisingly, actually inhibits the rate of cell death. As a control, we also apply the model to data describing the time- and dose-dependent effects of doxorubicin since its mechanism of action is better characterised.