Jlab experiment E04-018 was approved in 2004 to do measurements of elastic electron scattering off the ³He and ⁴He few-body systems up to the highest momentum transfers possible, limited by cross section sensitivity. The measurements will extend our knowledge of the elastic form factors of the helium isotopes down by more than one order in magnitude and out in Q² possibly by more than a factor of two. The experiment will use the Hall A Facility of Jlab. Scattered electrons will be detected in the Electron High Resolution Spectrometer. Electron-recoil nucleus coincidences will be identified by double- arm time-of-flight. The effective double-arm solid angle and radiative corrections for the evaluation of the cross sections will be determined by means of a Monte Carlo simulation. The results are expected to play a crucial role in establishing a consistent standard model describing the structure of few-body nuclei in terms of nucleons and mesons, and in possibly providing evidence for its break-down at "large" momentum transfers, where the quark-gluon degrees of freedom are expected to dominate.