The Sterile Insect Technique (SIT) is a biological control technique based on mass-rearing, radiation-based sterilization that can induce fitness costs, and releases of the pest species targeted for population control. Sterile matings, between females and sterilized males, can reduce the overall population growth rate and cause a fall in population density. However, a proportion of irradiated males may escape sterilization, which is termed residual fertility. Our aim in this paper is to study the impact of residual fertility on pest control, by a modeling approach. We modeled the pest population dynamics with three generic differential equations representing sterilized males, wild males and wild females. We explored the impact of residual fertility, associated or not with fitness costs, on pest control possibilities as compared to a situation in which male sterilization is flawless. We carried out a detailed mathematical analysis of the model dynamics through the computation of its equilibria and their stability. Bifurcation analyses were performed with parameters calibrated on the Mediterranean fruit fly Ceratitis capitata.. We showed that when residual fertility is below a threshold value, wild populations can be driven to extinction by flooding the landscape with sterilized males. This threshold is higher when residual fertility is associated with fitness costs. Too high a level of residual fertility makes SIT less effective and hinders population eradication. Nevertheless, substantial decreases in outbreak levels can still be achieved for much larger residual fertility rates.