Polygenic risk scores (PRSs) have been offered since 2019 to screen in vitro fertilization embryos for genetic liability to adult diseases, despite a lack of comprehensive modeling of expected outcomes. Here we predict, based on the liability threshold model, the expected reduction in complex disease risk following polygenic embryo screening for a single disease. A strong determinant of the potential utility of such screening is the selection strategy, a factor that has not been previously studied. When only embryos with a very high PRS are excluded, the achieved risk reduction is minimal. In contrast, selecting the embryo with the lowest PRS can lead to substantial relative risk reductions, given a sufficient number of viable embryos. We systematically examine the impact of several factors on the utility of screening, including: variance explained by the PRS, number of embryos, disease prevalence, parental PRSs, and parental disease status. We consider both relative and absolute risk reductions, as well as population-averaged and per-couple risk reductions, and also examine the risk of pleiotropic effects. Finally, we confirm our theoretical predictions by simulating ‘virtual’ couples and offspring based on real genomes from schizophrenia and Crohn’s disease case-control studies. We discuss the assumptions and limitations of our model, as well as the potential emerging ethical concerns.