Abstract: For the torsional vibration problem of a single pile in soil, the constitutive relationship of the pile around soil was described by Kelvin viscoelastic model, three-parameters viscoelastic model and fractional derivative viscoelastic (FDV) model, and the torsional vibration of the soil and the pile were also solved, respectively. The torsional vibration of a single pile in soil described by the three viscoelastic models were investigated, and the influences of the parameters on the torsional vibration were discussed. The results indicated that the fluctuation of the curves of the real and imaginary part of torsional complex stiffness of pile in soil described by three-parameters solid model varying with frequency was smaller than that of the other two models, the characteristics of torsional vibration of a single pile in viscoelastic soil had related with the constitutive relationship of the soil, and the torsional complex stiffness of the pile in the soil described by classic viscolestic model was larger than that of the soil described by fractional derivative viscoelastic model