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　analytic　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　analytical　approximate　periodic　solutions　for　MDOF　nonlinear　dynamic　system.　The　periodic　solutions　for　the　parametric　excitation　buckled　thin　plate　system　of　MDOF　are　applied　to　illustrate　the　validity　and　great　potential　of　this　method.　In　addition,　comparisons　are　conducted　between　the　results　obtained　by　the　EHAM　and　the　numerical　integration　(i.e.　Runge-Kutta)　method.　It　is　shown　that　the　second-order　analytical　solutions　of　the　EHAM　agree　well　with　the　numerical　integration　solutions,　even　if　time　t　progresses　to　a　certain　large　domain　in　the　time　history　responses.　Copyright　©　2010　by　ASME.