This paper deals with the spin-polarization change of an electron beam after elastic scattering with a neutral atom. The first part of the paper is devoted to summarizing the Kessler theory of the elastic scattering of spin-polarized electron beams. After a general description of the dependence on the polar and azimuthal angles of the spin-polarization after scattering, the effects on the spin-polarization of multiple elastic collisions occurring in the same scattering plane and with identical scattering angles are also treated. In particular, we show that, in this case, an initially unpolarized beam becomes fully polarized in the direction normal to the scattering plane after a number of collisions. The number of collisions necessary to reach full (transverse) polarization is a function of the common scattering angle. We also demonstrate that spin-polarization is conserved for forward and backward elastic scattering.