Despite clinical observations of cardiotoxicity among cancer patients treated with tyrosine kinase inhibitors (TKIs), the molecular mechanisms by which these drugs affect the heart remain largely unknown. Mechanistic understanding of TKI-induced cardiotoxicity has been limited in part due to the complexity of tyrosine kinase signaling pathways and the multi-targeted nature of many of these drugs. TKI treatment has been associated with reactive oxygen species generation, mitochondrial dysfunction, and apoptosis in cardiomyocytes. To gain insight into the mechanisms mediating TKI-induced cardiotoxicity, this study constructs and validates a computational model of cardiomyocyte apoptosis, integrating intrinsic apoptotic and tyrosine kinase signaling pathways. The model predicts high levels of apoptosis in response to sorafenib, sunitinib, ponatinib, trastuzumab, and gefitinib, and lower levels of apoptosis in response to nilotinib and erlotinib, with the highest level of apoptosis induced by sorafenib. Knockdown simulations identified AP1, ASK1, JNK, MEK47, p53, and ROS as positive functional regulators of sorafenib-induced apoptosis of cardiomyocytes. Overexpression simulations identified Akt, IGF1, PDK1, and PI3K among the negative functional regulators of sorafenib-induced cardiomyocyte apoptosis. A combinatorial screen of the positive and negative regulators of sorafenib-induced apoptosis revealed ROS knockdown coupled with overexpression of FLT3, FGFR, PDGFR, VEGFR, or KIT as a particularly potent combination in reducing sorafenib-induced apoptosis. Network simulations of combinatorial treatment with sorafenib and the antioxidant N-acetyl cysteine (NAC) suggest that NAC may protect cardiomyocytes from sorafenib-induced apoptosis.