A fully recycled carbon fibre reinforced polypropylene (rCF/rPP) composite material has been developed and characterised. This new, randomly oriented short fibre composite was manufactured by press forming with a fibre volume fraction of 40 %. A series of tensile tests using rectangular specimens cut in four different directions (0°, 90°, ±45°) in the composite plate were performed to confirm in-plane material isotropy. Models to predict stiffness and strength of the short fibre rCF/rPP composite were also employed and validated using experiments. To model the viscoelastic and viscoplastic responses of the composite, an inelastic material model was employed and characterised using a series of creep and recovery tests. From the creep tests, it was found that the time and stress dependence of viscoplastic strains follows a power law. The viscoelastic response of the composite was found to be linear in the investigated stress range. The material model was validated in constant stress rate tensile tests and the agreement was good, even close to the rupture stress.