A mathematical model is proposed for polymer solution flow in dead-end pores, which was studied using micro-seepage of polymer solutions as an example. The mathematical model, including a continuity equation, a momentum conservation equation, and an equation of state, was solved by the finite difference method. The stream function and velocity contours were determined. The micro sweep efficiency when flooding the formation was calculated based on the velocity contour. The influence of elasticity, flow velocity, and viscosity of the polymer solution on the micro sweep efficiency was evaluated. It is demonstrated that the viscosity and the injection rate have a lesser effect on micro sweep efficiency than the elasticity of the polymer solution.