Based on analysis of viscous-elastic polymer solution flowing in the throat, the flowing process is divided into entrance constriction, passing pore-passage and extrusion, and the pressure drop in every stage is separated into viscous drop and elastic drop. Mathematical pressure drop expressions of every stage are established using tensor analysis in consideration of pseudo plasticity, elastic properties, elastic recovery characteristic, pore throat ratio and porosity factor, and the viscous-elastic constitutive model is established considering polymer's characteristic and porous media's feature. According to the new constitutive model, the unsteady flowing mathematical model is established and solved employing numerical method. The influences of relaxation time, consistency coefficient, power law index, porosity factor and injection rate on pressure performance are analyzed, and the typical curves are drew. The results show, the injection pressure increases with the increase of relaxation time, consistency coefficient and injection rate, and decreases with the increase of power law index and porosity factor.
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