Cascading　failures　on　interdependent　networks　have　attracted　much　attention　in　recent　years.　In　this　paper,　we　study　a　cascading　failure　model　on　interdependent　networks　with　multiple　dependency　relations　and　cliques,　in　which　a　clique　is　dependent　on　multiple　cliques　in　other　network　and　all　nodes　in　the　same　clique　are　survive　or　fail　together.　Through　a　percolation　theory,　we　find　that　the　system　always　undergoes　a　first　order　phase　transition　when　the　dependency　relations　are　small.　The　robustness　of　the　system　increases　with　increasing　the　number　of　multiple　dependency　relations　between　two　networks　and　the　size　of　cliques.　The　theory　can　well　predict　the　numerical　simulations.　(C)　2019　Elsevier　B.V.　All　rights　reserved.