  A theoretical description of elastic polarized muon-electron scattering is
presented. Complete one-loop electroweak radiative corrections are calculated
with taking into account the exact dependence on the muon mass. The effects due
to some higher order corrections and the electroweak scheme dependence are
analyzed. The case of longitudinally polarized fermions in the initial state is
investigated. Analytical results are derived with the help of the SANC system.
Numerical results are presented for unpolarized and polarized cross sections.
Calculations are realized in the Monte Carlo integrator MCSANCee and generator
ReneSANCe which allow the implementation of any experimental cut used in the
analysis of elastic $\mu - e$ scattering data.
