The dynamic of cancer is intimately linked to a dysregulation of the cell cycle and signalling pathways. It has been argued that selectivity of treatments could exploit loss of checkpoint function in cancer cells, a concept termed cyclotherapy. Quantitative approaches that describe these dysregulations can provide guidance in the design of novel or existing cancer therapies. We describe and illustrate this strategy via a mathematical model of the cell cycle that includes descriptions of the G1-S checkpoint and the spindle assembly checkpoint (SAC), the EGF signalling pathway and apoptosis. We incorporated sites of action of four drugs (palbociclib, gemcitabine, paclitaxel and actinomycin D) to illustrate potential applications of this approach. We show how drug effects on multiple cell populations can be simulated, facilitating simultaneous prediction of effects on normal and transformed cells. The consequences of aberrant signalling pathways or of altered expression of pro- or anti-apoptotic proteins can thus be compared. We suggest that this approach, particularly if used in conjunction with pharmacokinetic modelling, could be used to predict effects of specific oncogene expression patterns on drug response. The strategy could be used to search for synthetic lethality and optimise combination protocol designs.