Abstract: Four KBKZ integral-type constitutive equations, includingWagner model, PSM model, 2e model and 3r model proposed by the authors, wereused in the paper to describe the viscoelastic characteristics of a Bogerfluid. The least square approximation was adopted to fit G' and G''to obtain the relaxation spectrum of the fluid, and the nonlinearprogramming method was employed to fit N_1 to obtain the parametervalues in the damping function of the four models. The results show that thefour models can characterize the rheological properties of the Boger fluidprecisely. Either Wagner model or PSM model is a good choice forcharacterizing the viscoelastic properties of Boger fluid, due to its simplicity.