The mechanism of viscoelastic polymer solution flooding is very complicated. In order to further improve the flooding effect and improve the flooding mechanism, the flow characteristics of viscoelastic polymer solution under different models were developed. In order to study the microscopic flow characteristics of polymer solution, this paper studies the typical reservoir porous model-sudden shrinkage channel model. Phan-thine-tanner (PTT) model, Upper-Convected Maxwell constitutive model, Oldroyd-B model are selected to establish a two-dimensional, steady and isothermal mathematical model of fluid flow. The finite difference numerical method is applied to solve the mathematical model, the stream function contours, velocity contours are drawn. The effect of the parameters of viscoelastic polymer solution on the flow characteristics was studied, and the effect of viscoelasticity on the microcosmic sweep efficiency was analyzed.