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An analytical investigation of the squeak in the mechanical seal used in water pumps is presented in this paper. The squeak investigated in this paper is generated by self-excited torsional vibration of the rotational shaft of the water pump, and is caused by the stick-slip phenomenon of the mechanical seal. The fundamental cause is the friction characteristic of the seal. In addition to the seal friction characteristic, the effects of other parameters: shaft dimensions, rotor inertial moment and seal attachment position, have been analyzed in this paper. The simulation model was constructed using an equivalent vibration system obtained from the natural torsional mode shape of the shaft and its kinetic energy. It was confirmed that the stability of the stick-slip self-excited vibration, which generates the squeak, could be predicted using the simulation model.