This　paper　focuses　on　the　problem　of　nonlinear　dynamic　response　variability　resulting　from　stochastic　system　properties　and　random　loads.　An　efficient　and　accurate　method,　which　can　be　employed　to　analyze　the　dynamic　responses　of　random　finite　element　systems　with　local　nonlinearity,　is　presented　in　this　paper.　This　method,　dubbed　as　the　partition　expansion　method,　is　based　on　the　partitioned　time　integration　algorithm　in　conjunction　with　the　Neumann　expansion　technique　within　the　framework　of　the　Monte　Carlo　simulation.　Two　numerical　examples　involving　structural　and　mechanical　stochastic　vibration　problems　are　employed　to　illustrate　the　advantage　of　the　proposed　method　with　respect　to　accuracy　and　efficiency.　By　comparing　the　results　obtained　by　the　direct　Monte　Carlo　simulation,　the　dynamic　response　statistics　can　be　accurately　determined　using　the　proposed　method　with　four　order　expansion　while　the　computational　efforts　are　significantly　reduced.　The　comparison　of　computing　time　indicates　that　the　proposed　method　is　efficient　and　practical　for　analyzing　the　statistical　quantities　of　stochastic　dynamic　systems　with　local　nonlinearity.