[en] Vlasov and drift kinetic simulation methods based on the symplectic integrators are benchmarked for test problems on the linear and nonlinear Landau dampings and the Kelvin-Helmholtz (K-H) instability. The explicit symplectic integrator for the separable Hamiltonian straightforwardly leads to generalization of the splitting scheme for the Vlasov-Poisson system. The Nth-order version improves the total energy conservation decreasing the error as ∝ Δt^N where Δt denotes the time step size. An Eulerian drift kinetic simulation scheme derived from the implicit symplectic integrator for the non-separable Hamiltonian exactly satisfies the conservation of the energy and the enstrophy in the K-H instability, and results in successful application to the plasma echo. (author)