Genital herpes, caused by herpes simplex virus, is the most prevalent sexually transmitted disease worldwide. In many developing countries genital herpes is untreated, and in the United States only 10% of cases are treated. We present a mathematical model that we use as a health policy tool to predict the levels of antiviral drug resistance that would emerge, if treatment rates were increased, and to identify the key factors in determining the emergence of drug resistance. We use our results to suggest control measures for herpes epidemics that would prevent the emergence of substantial levels of antiviral drug resistance.