In normal circumstances, many practical engineering problems are nonlinear and can be described by multi-degree-of-freedom (MDOF) dynamical systems.Theoretically speaking, the exact solutions are very scarce.so it is extremely significant to develop the anal.vtic tools for nonlinear systems in engineering.Inasmuch as the homotopy analysis method (HAM) can overcome the foregoing restrictions of conventional perturbation techniques, this method has been widely applied to solve a variety of nonlinear problems.In this paper, the extended homotopy analysis method (EHAM) is presented to establish the anal.vtical approximate periodic solutions for MDOF nonlinear dynamic system.The periodic solutions for the parametrically and externally excited buckled thin plate system of MDOF are applied to illustrate the validity and great potential of this method.