  The classical equation of motion of a charged point particle, including its
radiation reaction, is described by the Lorentz-Dirac equation. We found a new
class of solutions that describe tunneling (in a completely classical
context!). For nonrelativistic electrons and a square barrier, the solution is
elementary and explicit. We show the persistance of the solution for smoother
potentials. For a large range of initial velocities, initial conditions may
leave a (discrete) ambiguity on the resulting motion.
