Environmental stress screening (ESS) is widely used in industry to eliminate early or latent failures. However, the appropriate stochastic modeling for ESS has not been yet suggested in the literature. In this paper, we develop the corresponding stochastic model and analyze the effect of the ESS in terms of population characteristics. In our model, during the ESS, the manufactured items are exposed to a stress with the relatively large magnitude, which can result either in immediate failures of items or in the increased susceptibility to future failures. The corresponding optimization problems for obtaining the optimal level of the stress magnitude are also formulated and discussed. An illustrative example is considered. (C) 2015 Elsevier Ltd. All rights reserved.