  The initial insight into electron elastic scattering off endohedral
fullerenes A@C60 is gained in the framework of a theoretical approach where the
C60 cage is modelled by a rectangular (in the radial coordinate) potential
well, as in many other A@C60 studies. The effect of a noticeably weaker
electron elastic scattering off A@C60 compared to that off empty C60 or even
the isolated atom A itself, as well as a strong sensitivity of e + A@C60
scattering to the spin of the captured atom A are unraveled, for certain kinds
of atoms. Obtained results lay out the initial qualitative basis for
identifying interesting measurements and/or more rigorous calculations of e +
A@C60 elastic scattering to perform.
