Lethal mutagenesis is a broad-spectrum antiviral strategy that exploits the high mutation rate and low mutational tolerance of many RNA viruses. This approach uses mutagenic drugs to increase viral mutation rates and burden viral populations with mutations that reduce the number of infectious progeny. We investigated the effectiveness of lethal mutagenesis as a strategy against influenza virus using three nucleoside analogs, ribavirin, 5-azacytidine, and 5-fluorouracil. All three drugs were active against a panel of seasonal H3N2 and laboratory-adapted H1N1 strains. We found that each drug increased the frequency of mutations in influenza virus populations and decreased the virus´ specific infectivity, indicating a mutagenic mode of action. We were able to drive viral populations to extinction by passaging influenza virus in the presence of each drug, indicating that complete lethal mutagenesis of influenza populations can be achieved when a sufficient mutational burden is applied. Population-wide resistance to these mutagenic agents did not arise after serial passage of influenza populations in sub-lethal concentrations of drug. Sequencing of these drug-passaged viral populations revealed genome-wide accumulation of mutations at low frequency. The replicative capacity of drug-passaged populations was reduced at higher multiplicities of infection, suggesting the presence of defective interfering particles and a possible barrier to the evolution of resistance. Together, our data suggest that lethal mutagenesis may be a particularly effective therapeutic approach with a high genetic barrier to resistance for influenza virus.