This　paper　develops　a　3D　base　force　element　method　(BFEM)　based　on　the　potential　energy　principle.　According　to　the　BFEM,　the　stiffness　matrix　and　node　displacement　of　any　eight-node　hexahedral　element　are　derived　as　a　uniform　expression.　Moreover,　this　expression　is　explicitly　expressed　without　a　Gaussian　integral.　A　3D　random　numerical　model　of　recycled　aggregate　concrete　(RAC)　is　established.　The　randomness　of　aggregate　was　obtained　by　using　the　Monte　Carlo　random　method.　The　effects　of　the　recycled　aggregate　substitution　and　adhered　mortar　percentage　on　the　elastic　modulus　and　compressive　strength　are　explored　under　uniaxial　compression　loading.　In　addition,　the　failure　pattern　is　also　studied.　The　obtained　data　show　that　the　3D　BFEM　is　an　efficient　method　to　explore　the　failure　mechanism　of　heterogeneous　materials.　The　3D　random　RAC　model　is　feasible　for　characterizing　the　mesostructure　of　RAC.　Both　the　substitution　of　recycled　aggregate　and　the　percentage　of　adhering　mortar　have　a　non-negligible　influence　on　the　mechanical　properties　of　RAC.　As　the　weak　points　in　the　specimen,　the　old　interfacial　transition　zone　(ITZ)　and　adhered　mortar　are　the　major　factors　that　lead　to　the　weakened　properties　of　RAC.　The　first　crack　always　appears　in　these　weak　zones,　and　then,　due　to　the　increase　and　transfer　of　stress,　approximately　two-to-three　continuous　cracks　are　formed　in　the　45　degrees　direction　of　the　specimen.