  It is known that some high-energy processes have a $t$-channel singularity in
the physical region. In this paper we show that this singularity is regularized
if one takes into account the finite sizes of the colliding beams, i.e. the
realistic situation which takes place at high--energy colliders. On this way we
obtain the finite cross section which is linear proportional to the transverse
sizes of the colliding beams. As an application of the above result we study
the production of the single $W$ boson at $\mu^+\mu^-$ colliders in the
reaction $\mu ^- \mu ^+ \to e \bar \nu _e W^+ $. For the total energy $\sqrt
{s}\approx 95$ GeV and reasonable parameters of the muon beams the ``beam--size
'' dependent part of the cross section for this reaction is of the order of the
standard cross section of the $\mu ^- \mu ^+ \to \mu^- \bar \nu _{\mu} W^+ $
process.
