A method of electropolishing an internal passageway of a component, wherein the passageway has an inlet and an outlet; including: providing an electrode assembly including a flexible electrode, a shuttle and a guide cable extending between the flexible electrode and the shuttle; inserting the shuttle into the inlet; causing fluid to flow through the passageway to transport the shuttle through the passageway from the inlet towards the outlet; pulling the guide cable through the passageway to position the electrode in the passageway adjacent to a region of the passageway to be polished; and electropolishing the passageway using the electrode while moving the electrode within the passageway. Also, an electrode assembly for electropolishing an internal passageway of a component, including: a flexible electrode, a shuttle, and a guide cable extending between the flexible electrode and the shuttle.