Autophagy is a conserved biological stress response in mammalian cells that is responsible for clearing damaged proteins and organelles from the cytoplasm and recycling their contents via the lysosomal pathway. In cases of mild stress, autophagy acts as a survival mechanism, while in cases of severe stress cells may switch to programmed cell death. Understanding the decision process that moves a cell from autophagy to apoptosis is important since abnormal regulation of autophagy occurs in many diseases, including cancer. To integrate existing knowledge about this decision process into a rigorous, analytical framework, we built a mathematical model of cell fate decisions mediated by autophagy. Our dynamical model is consistent with existing quantitative measurements of autophagy and apoptosis in rat kidney proximal tubular cells responding to cisplatin-induced stress.