Abstract: The geometricintegration method of dynamical systems has been an attractivedirection in the last two decades. Dynamic equations of multibodysystems, such as differential equation and differential-algebraicequation, are a kind of representative dynamical systems. Thesignificance of the transformation from Lagrange framework toHamilton framework is the configuration transformation fromEuclidian to Hamiltonian. The symplectic variable is introducedinto the mechanics system, and thus the symplectic integrationmethod can be adopted to solve the dynamic equations. Certainqualitative information of the multibody dynamic system can bepredicted and is expected to be maintained in the process ofdiscretization, which is of particular significance when thisqualitative information indicates key physical meaning. How toestablish proper Hamiltonian canonical equations of the multibodysystem (multi-rigid body system without constraint or withholonomic constraint, flexible multibody system) is brieflydescribed, with emphases laid on the formulation of geometricintegral methods, especially the computational geometric mechanicsmethods with promising applications, such as the high-ordersymplectic algorithm (synthesized algorithm, Partition-synthesizedalgorithm, symplectic precise integration algorithm),multi-symplectic algorithm and Lie group algorithm (projectedmethod and located coordination method).