  We discuss, in the context of classical electrodynamics with a Lorentz
invariant cut-off at short distances, the self-force acting on a point charged
particle. It follows that the electromagnetic mass of the point charge occurs
in the equation of motion in a form consistent with special relativity. We find
that the exact equation of motion does not exhibit runaway solutions or
non-causal behavior, when the cut-off is larger than half of the classical
radius of the electron.
