Succinate dehydrogenase (SDH) is an inner mitochondrial membrane protein complex that links the Krebs cycle to the electron transport system. It can produce significant amounts of superoxide (O2.-) and hydrogen peroxide (H2O2); however, the precise mechanisms are unknown. This fact hinders the development of next-generation antioxidant therapies targeting mitochondria. To help address this problem, we developed a computational model to analyze and identify the kinetic mechanism of O2.- and H2O2 production by SDH. Our model includes the major redox centers in the complex, namely FAD, three iron-sulfur clusters, and a transiently bound semiquinone. Oxidation state transitions involve a one- or two-electron redox reaction, each being thermodynamically constrained. Model parameters were simultaneously fit to many data sets using a variety of succinate oxidation and free radical production data. In the absence of respiratory chain inhibitors, model analysis revealed the 3Fe-4S iron-sulfur cluster as the primary O2.- source. However, when the quinone reductase site is inhibited or the quinone pool is highly reduced, O2.- is generated primarily by the FAD. In addition, H2O2 production is only significant when the enzyme is fully reduced, and fumarate is absent. Our simulations also reveal that the redox state of the quinone pool is the primary determinant of free radical production by SDH. In this study, we showed the importance of analyzing enzyme kinetics and associated side-reactions in a consistent, quantitative, and biophysically detailed manner using a diverse set of experimental data to interpret and explain experimental observations from a unified perspective.