Abstract: In this paper, two dimensional Stokes flow are reduced to the determination of eigenvalues andeigensolutions with the aid of Hamiltonian system. The close method of the symplectic enginsolution ispresented based on the completeness of the space of symplectic enginsolutions. The results explain that basicflows can be described by zero-enginvalue enginsolutions and end effects for Stokes flow by enginsolutions ofnon-zero-enginvalues. Numerical results reveal some rules of symplectic enginvalues and enginsolutions.Numerical examples show that the irregular flow of the ends of the pipeline is decayed. At the same time, themethod is a path for solving the other problem.Key Words: Stokes flow；Incompressible fluid； Hamiltonian system； symplectic