The　tensile　constitutive　relationship　is　essential　for　determining　the　ductility　and　restoring　force　characteristics　of　seismic-resistant　concrete　structures　and　studying　the　mechanisms　causing　damage　and　fracture　to　concrete　structures.　This　study　investigates　the　axial　tensile　stress–strain　curves　of　mortar,　the　interface　between　new　and　old　mortar,　and　recycled　aggregate　concrete　(RAC)　with　different　water-binder　ratios　and　ages.　First,　the　tensile　constitutive　relationships　of　mortar　and　new-old　mortar　interface　were　established.　Then,　based　on　the　experimental　results　and　the　random　aggregate　model,　a　double-interface　numerical　model　of　RAC　was　established　to　investigate　the　development　of　tensile　damage　in　RAC　and　the　influence　law　and　mechanism　of　the　old　mortar　strength,　thickness　and　curing　age　on　the　curve　of　the　tensile　stress–strain　of　RAC.　The　results　are　a　comparison　of　the　peak　tensile　strengths　at　the　same　age　and　water-binder　ratio　for　the　above　three　mortar　types,　where　new　mortar　＞　RAC　＞　new-old　mortar　interface.　Under　the　same　thickness　of　old　mortar,　the　peak　stress,　elastic　modulus　and　peak　cutline　modulus　of　RAC　increased　with　the　increase　of　old　mortar　strength,　and　the　amplitude　of　change　increased　with　the　increase　of　mortar　thickness.　Based　on　the　tensile　constitutive　relationship　of　ordinary　concrete,　the　tensile　constitutive　relationship　of　recycled　coarse　aggregate　concrete　is　proposed　by　combining　the　experimental　results　and　numerical　analysis　results.　©　2023　Elsevier　Ltd