The　size　effect　and　macroscopic　mechanical　nonlinearity　of　concrete　are　caused　by　its　inherent　heterogeneity.　Considering　the　mesoscopic　structure,　concrete　is　treated　as　a　composite　material　consisting　of　aggregate,　mortar　matrix　and　an　interfacial　transition　zone　(ITZ).　The　double-line　elastic-damage　model　has　been　borrowed　to　describe　the　mechanical　properties　of　the　mortar　matrix　and　the　ITZs.　Aggregate　is　assumed　to　be　elastic,　so　it　cannot　be　damaged.　Then,　a　general　expression　of　the　length　of　the　fracture　crack　propagation　path　and　a　theoretical　solution　for　the　uniaxial　tensile　strength　for　different　graded　concretes　are　established.　Finally,　the　theoretical　resolution　is　compared　with　the　simulation　results　at　meso-scale　and　the　rationality　of　the　theoretical　formulae　for　crack　length　and　tensile　strength　from　the　present　work　is　thereby　validated.　©　2017,　Engineering　Mechanics　Press.　All　right　reserved.