The　base　force　element　method　(BFEM)　on　damage　mechanics　is　used　to　analyze　the　compressive　strength,　the　size　effects　of　compressive　strength,　and　fracture　process　of　concrete　at　mesolevel.　The　concrete　is　taken　as　three-phase　composites　consisting　of　coarse　aggregate,　hardened　cement　mortar,　and　interfacial　transition　zone　(ITZ)　on　mesolevel.　The　random　aggregate　model　is　used　to　simulate　the　mesostructure　of　concrete.　The　mechanical　properties　and　fracture　process　of　concrete　under　uniaxial　compression　loading　are　simulated　using　the　BFEM　on　damage　mechanics.　The　simulation　results　agree　with　the　test　results.　This　analysis　method　is　the　new　way　for　investigating　fracture　mechanism　and　numerical　simulation　of　mechanical　properties　for　concrete.