Widespread resistance among circulating influenza A strains to at least one of the anti-influenza drugs is a major public health concern. A triple combination antiviral drug (TCAD) regimen comprised of amantadine, oseltamivir, and ribavirin has been shown to have synergistic and broad spectrum activity against influenza A strains, including drug resistant strains. Here, we used mathematical modeling along with three different experimental approaches to understand the effects of single agents, double combinations, and the TCAD regimen on resistance in influenza in vitro, including: 1) serial passage at constant drug concentrations, 2) serial passage at escalating drug concentrations, and 3) evaluation of the contribution of each component of the TCAD regimen to the suppression of resistance. Consistent with the modeling which demonstrated that three drugs were required to suppress the emergence of resistance in influenza A, treatment with the TCAD regimen resulted in the sustained suppression of drug resistant viruses, whereas treatment with amantadine alone or the amantadine-oseltamivir double combination led to the rapid selection of resistant variants which comprised ∼100% of the population. Furthermore, the TCAD regimen imposed a high genetic barrier to resistance, requiring multiple mutations in order to escape the effects of all the drugs in the regimen. Finally, we demonstrate that each drug in the TCAD regimen made a significant contribution to the suppression of virus breakthrough and resistance at clinically achievable concentrations. Taken together, these data demonstrate that the TCAD regimen was superior to double combinations and single agents at suppressing resistance, and that three drugs at a minimum were required to impede the selection of drug resistant variants in influenza A virus. The use of mathematical modeling with multiple experimental designs and molecular readouts to evaluate and optimize combination drug regimens for the suppression of resistance may be broadly applicable to other infectious diseases.