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We use publicly available N-body simulations and semi-analytic models of galaxy formation to estimate the levels of external shear due to structure near the lens in gravitational lens systems. We also describe two selection effects, specific to four-image systems, that enhance the probability of observing systems to have higher external shear. Ignoring additional contributions from "cosmic shear" and assuming that lens galaxies are not significantly flattened, we find that the mean shear at the position of a quadruple lens galaxy is 0.11, the rms shear is roughly 0.15, and there is roughly a 45% likelihood of external shear greater than 0.1. This is much larger than previous estimates and in good agreement with typical measured external shear. The higher shear primarily stems from the tendency of early-type galaxies, which are the majority of lenses, to reside in overdense regions.
Holder et al. (Sun,) studied this question.