The　stochastic　free　vibration　characteristics　of　a　functionally　graded　material　(FGM)　beam　with　material　properties　graded　across　spatial　position　are　examined　in　this　paper,　in　which　both　physical　parameters　of　each　constituent　material　and　volume　fraction　index　denoting　material　distribution　are　treated　as　random　variables　with　low　variability.　Integrating　random　variables　into　modelling　by　using　the　first-order　perturbation　technique,　a　stochastic　finite　element　model　is　developed　for　the　FGM　beam　and　the　direct　relationship　is　derived　between　the　first-derivatives　of　structural　modal　frequencies　and　mode　shapes　with　respect　to　random　variables　and　those　of　the　FGM　effective　material　properties　with　respect　to　random　variables.　The　material　graduation　in　FGMs　is　represented　by　power-law　function.　Comparing　with　the　Monte-Carlo　simulation,　the　influence　of　constituent　material　properties,　material　distribution　and　slenderness　ratio　on　the　statistics　of　free　vibration　characteristics　for　the　FGM　beam　is　systemically　examined.　The　results　show　that　the　randomness　coming　from　constituent　material　physical　properties　contributes　much　more　to　the　scatterings　of　modal　parameters　than　the　randomness　from　material　distribution　while　material　distribution　plays　an　important　role　in　the　stochastic　study　of　the　structure,　and　the　slenderness　ratio　has　significant　effect　on　the　mean　values　of　both　modal　frequencies　and　mode　shapes.　(C)　2016　Elsevier　Inc.　All　rights　reserved.