The dynamic design object of rotor system is to optimize the system in stability at the operating speed, unbalance response in the vicinity of the rotor critical speed, bearing weighting and system weighting. In conventional optimization method, designers have to set mathematical modeling, such as objective function, constraints and design parameters, strictly and quantitavely. But in actual design process, they do not treat all of these values strictly and some of them are somehow "fuzziness". So, considering boundary conditions of seal diameter, clearance, and length in a typical double suction centrifugal pump is fuzzy, this paper is considered fuzzy in constraints. Fuzzy method is used .alpha.-level cut method. Then, the optimum dimensions of seal according to values are obtained and vibration characteristics are investigated.estigated.