The emergence of resistance against drugs that inhibit a particular protein is a major problem in targeted therapy. There is a clear need for rigorous methods to predict the likelihood of specific drug-resistance mutations arising in response to the binding of a drug. In this work we attempt to develop a robust computational protocol for predicting drug resistant mutations at the gatekeeper position (T790) in EGFR. We explore how mutations at this site affects interactions with ATP and three drugs that are currently used in clinics. We found, as expected, that certain mutations are not tolerated structurally, while some other mutations interfere with the natural substrate and hence are unlikely to be selected for. However, we found five possible mutations that are well tolerated structurally and energetically. Two of these mutations were predicted to have increased affinity for the drugs over ATP, as has been reported earlier. By reproducing the trends in the experimental binding affinities of the data, the methods chosen here are able to correctly predict the effects of these mutations on the binding affinities of the drugs. However, the increased affinity does not always translate into increased efficacy, because the efficacy is affected by several other factors such as binding kinetics, competition with ATP, and residence times. The computational methods used in the current study are able to reproduce or predict the effects of mutations on the binding affinities. However, a different set of methods is required to predict the kinetics of drug binding.