Chopped　aramid　fibre-reinforced　rubber　composite　(AFRC)　is　widely　used　in　industry　owing　to　its　excellent　characteristics.　Rubber’s　mechanical　properties　vary　with　the　addition　of　aramid　fibres.　Although　hyperelastic　constitutive　models　exist　for　unfilled　and　filled　rubber　with　carbon　black,　constitutive　models　for　AFRCs　have　not　been　investigated　yet.　Here,　we　present　experimental　results　demonstrating　the　stress–strain　responses　of　AFRC,　together　with　the　Mullins　effect,　under　both　uniaxial　and　equibiaxial　tensile　loadings.　The　existing　classical　hyperelastic　constitutive　models　and　the　model　proposed　here　were　applied　to　AFRC.　Unlike　the　existing　model,　the　proposed　model　requires　fewer　variables　in　the　energy　function　and　permits　further　study　of　the　stress-softening　mechanism　of　AFRC.　Finally,　the　pseudo-elastic　(PE)　model　was　applied　to　AFRC,　revealing　that　the　damage　parameters　exhibited　a　linear　relationship　with　the　fibre　content.　The　PE　model　is,　therefore,　beneficial　for　predicting　the　stress　softening　behaviour　of　AFRC.　©　2020　Institute　of　Materials,　Minerals　and　Mining　Published　by　Taylor　&　Francis　on　behalf　of　the　Institute.