We investigate the expected correlation between the weak gravitational shear of distant galaxies and the orientation of foreground galaxies , through the use of numerical simulations . This shear-ellipticity correlation can mimic a cosmological weak lensing signal , and is potentially the limiting physical systematic effect for cosmology with future high-precision weak lensing surveys . We find that , if uncorrected , the shear-ellipticity correlation could contribute up to 10 % of the weak lensing signal on scales up to 20 arcminutes , for lensing surveys with a median depth z _ { m } = 1 . The most massive foreground galaxies are expected to cause the largest correlations , a result also seen in the Sloan Digital Sky Survey . We find that the redshift dependence of the effect is proportional to the lensing efficiency of the foreground , and this offers prospects for removal to high precision , although with some model dependence . The contamination is characterised by a weakly negative B-mode , which can be used as a diagnostic of systematic errors . We also provide more accurate predictions for a second potential source of error , the intrinsic alignment of nearby galaxies . This source of contamination is less important , however , as it can be easily removed with distance information .