Consideramultidimensionalrenewalriskmodel,inwhichtheclaimsizes{Xk,k≥1}formasequenceofindependentandidenticallydistributedrandomvectorswithnonnegativecomponentsthatareallowedtobedependentoneachother.Theunivariatemarginaldistributionsofthesevectorshaveconsistentlyvaryingtailsandfinitemeans.Supposethattheclaimsizesandinter-arrivaltimescorrespondinglyformasequenceofindependentandidenticallydistributedrandompairs,witheachpairobeyingadependencestructure.Apreciselargedeviationforthemultidimensionalrenewalriskmodelisobtained.