A rod-like body made of a rubber material having an outside diameter which is substantially equal to the inside diameter of the guard pipe or an unexpanded resin material having a quality that the resin material expands sufficiently when heated in a paint baking process for the guard pipe is inserted, as a vibration damping material, into the interior of the guard pipe before the pipe is worked. Due to this, since the guard pipe can be made difficult to vibrate without making any substantial changes to the conventional vehicle body structure, the invention is effective in reducing noise generated while a vehicle is running without entraining a remarkable increase in production costs.