A nonlinear mathematical model of vertical transmission of HIV/AIDS is proposed to study the effects of drug resistance in the spread of the disease. The study assumes that treatment leads to the evolution of drug resistance in some pockets of the population. We use traditional methods to determine conditions for existence and stability of disease-free and endemic equilibrium points of the model. The study showed that the burden of the disease may be reduced if the reproduction number is reduced below unity and may persist if the reproduction number is raised above unity. Furthermore, evolution of drug resistance due to treatment may change the cause of the epidemic.