The finishing of turbine blisks, a critical technology determining the final geometric accuracy of blisks, can be implemented efficiently with the electrical discharge machining ( EDM). Upon the basis of the design of the electrode for blisk EDM finishing, the searching of an interference-free path for feeding an electrode through twist channels of a rimed blisk is carried out, in which the kernel problem is the determination of the electrode kinematic constraints. An implementation of the path-searching algorithm is illustrated with an example at the end of the paper.