Nowadays, biomedicine is a multidisciplinary science that requires a very broad approach to the study and analysis of various phenomena essential for a better understanding of human health. This study deals with the use of numerical simulations to better understand the processes of cancer viability and apoptosis in treatment with commercial chemotherapeutics. Starting from many experiments examining cell viability in real-time, determining the type of cell death and genetic factors that control these processes, a lot of numerical results were obtained. These in vitro test results were used to create a numerical model that gives us a new angle of observation of the proposed problem. Model systems of colon and breast cancer cell lines (HCT-116 and MDA-MB-231), as well as a healthy lung fibroblast cell line (MRC-5), were treated with commercial chemotherapeutics in this study. The results indicate a decrease in viability and the appearance of predominantly late apoptosis in the treatment, a strong correlation between parameters. A mathematical model was created and employed for a better understanding of investigated processes. Such an approach is capable of accurately simulating the behavior of cancer cells and reliably predicting the growth of these cells.