Non-steroidal anti-inflammatory drugs (NSAIDs) are one of the most commonly used classes of drugs. They target the cyclooxygenases (COX) 1 and 2 to reduce the physiological responses of pain, fever, and inflammation. Due to their role in inducing angiogenesis, COX proteins have also been identified as targets in cancer therapies. In this thesis, I describe computational protocols of molecular docking, molecular dynamics simulations and free energy calculations. These methods were used in this thesis to determine structure-activity relationships of a diverse set of NSAIDs in binding to their target proteins COX-1 and 2. Binding affinities were calculated and used to predict the binding modes. Based on combinations of molecular dynamics simulations and free energy calculations, binding mechanisms of sub-classes of NSAIDs were also proposed. Two stable conformations of COX were probed to understand how they affect inhibitor affinities. Finally, a brief discussion on selectivity towards either COX isoform is discussed. These results will be useful in future de novo design and testing of third-generation NSAIDs.