Abstract: The traditional solution methods of fluid mechanics, which were described based on one kind of variable, belong to the Euclidian space under the Lagrange system formulation. It is difficult to deal with some complex domain. In this paper, a new solution strategy for fluid mechanics is put forward. Dual variables and Hamiltonian function are introduced by variational principle such that a problem is promoted to symplectic geometrical space under the conservative Hamiltonian system. Furthermore, the solution based on the expansion of eigenvectors of Hamiltonian operator matrix is derived. The problem of three dimensional viscous flow with low Reynolds number is solved directly. Several basic solutions of fluid mechanics are obtained by virtue of solving the zero eigenvalue solutions and their Jordan normal forms. Finally, using the general solution named Papkovitch-Neuber, the edge effect of flow field is studied via solving the non-zero eigenvalue and superposing non-zero eigenvectors.