The systematic weak lensing of background galaxies by foreground galaxies has been detected by a number of different investigations. This effect is known as "galaxy–galaxy lensing" and it promises to provide strong constraints on the physical parameters of the dark matter halos which surround galaxies (such as their typical physical extents, total masses, and projected shapes). Here we use detailed Monte Carlo simulations to investigate galaxy–galaxy lensing by non–spherical dark matter halos and we estimate the area of a deep, ground–based imaging survey which would be required to detect the effects of flattened halos (〈∊〉 ~ 0.3) on the galaxy–galaxy lensing signal.