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In this paper, we focus on the sterile insect release technique (SIRT) in a predator--prey system with monotone functional response. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the predation population as a distinct dynamical equation together with the wild and sterile insect pests. The aim is to investigate the influence of the predation on the SIRT. We use both the continuous model and the impulsive model to carry out a theoretical study, discuss the dynamical behaviour of the model, and compute the critical conditions for eradication of wild insects. We get that both kinds of the predator-prey system with the most popular functional responses Holling type II and III and some other monotone response functions always have the wild insects eradication solution under the certain conditions. Our analytical findings are verified through computer simulation.