Understanding the genetic basis of HIV-1 drug resistance is essential for antiretroviral drug development. We analyzed drug resistant mutations in HIV-1 protease and reverse transcriptase under 18 drug treatments. The analysis is challenging because there is a large number of possible mutation combinations that may jointly affect drug resistance. The mutations are also strongly correlated, imposing inference difficulties such as multi-colinearity issues. We applied a novel Bayesian algorithm to the drug resistance data. Our method efficiently identified clusters of mutations in HIV-1 protease and reverse transcriptase that are strongly and directly associated with drug resistance. In addition to marginal associations, we detected strong interactions among mutations at distant protein locations. Most identified protein positions are crossresistant to several drugs of the same types. The effects of interactions are mostly negative, suggesting a threshold mechanism for the genetics underlying HIV drug resistance. Our method is among the first to produce detailed structures of marginal and interactive associations in HIV-1 drug resistance studies, and is generally suitable for detecting high-order interactions in large-scale datasets with complex dependencies.