Exceptional Elements(E.E) are generally eliminated by a machine duplication or a subcontract in cellular manufacturing system. One of the advantages in FMS consists of machines capable of multi-processing. This paper presents a method that eliminates E.Es by tool duplication. First, we develop the exceptional operation similarity(EOS) by machine cell-operation incidence matrix and part-operation incidence matrix. The EOS indicates a similarity of unperformable operations in each part when two exceptional parts are assigned to a machine cell. Secondly, a mathematical model to minimize tool duplication is developed by the EOS. Finally, a heuristic algorithm is developed to reflect dynamic situation in process of elimination of exceptional elements by the EOS and the mathematical model. A numerical example is provided to illustrate the algorithm.