The　geometry　of　the　attached　mortar　present　in　recycled　concrete　aggregates　influences　the　behaviour　of　recycled　aggregate　concrete,　since　this　mortar　is　porous,　rough　and　tends　to　increase　the　elongation　of　aggregate　particles.　These　factors　influence　shape,　volume,　and　complexity　of　the　mesoscopic　phases　of　concrete　(including　the　interfacial　transition　zone),　but　studies　on　this　topic　so　far　have　not　realistically　represented　the　geometry　and　mesoscopic　phases　of　recycled　aggregate　concrete.　This　hinders　a　proper　analysis　of　the　effect　of　the　attached　mortar＇s　geometry.　This　paper　develops　a　mesoscopic　model　for　recycled　aggregate　concrete,　considering　four　types　of　attached　mortar＇s　geometry　based　on　experimental　observation.　Concrete　mixes　numerically　modelled　with　either:　i)　the　four　attached　mortar＇s　geometries　combined　on　a　mixed　model　(representative　of　real　cases);　or　ii)　a　single　type　of　attached　mortar＇s　geometry　was　analysed　regarding　the　effect　of　the　attached　mortar＇s　geometry　on　the　compressive　and　tensile　behaviour　and　on　fracture　development.　The　main　findings　of　the　paper　are:　(1)　the　geometry　of　the　attached　mortar　is　relevant　to　the　behaviour　of　recycled　aggregate　concrete;　(2)　modelling　the　attached　mortar　as　present　in　both　ends　of　the　larger　radius　of　the　recycled　aggregate　leads　to　more　realistic　results;　(3)　modelling　the　attached　mortar　as　fully　enclosing　the　recycled　aggregate　overestimates　the　mechanical　properties.