The main purpose of this work consists of the mechanical characterization of a copolymer polypropylene (PP) filled with natural Alfa fibres. The elaboration of the PP-based composite reinforced with these natural fibres is explained. The mechanical behaviour of these composite blends has been analysed. Contrary to classical studies of the mechanical characterization of these kinds of materials which focus only on monotonic tensile tests, cyclic loading/unloading tests and loading/unloading tests interrupted by relaxation steps have been investigated. These tests enable us to compare the mechanical response of the virgin PP and the PP filled with Alfa fibres (Alfa/PP). Reinforcement by these natural fibres shows an impact in the improvement of the mechanical properties of this composite. All these experimental results constitute a data base used to identify the material parameters of a phenomenological constitutive hyperelasto-visco-hysteresis model. These tests also provide indications about the hyperelastic, viscous and hysteretic stress contributions of the hyperelasto-visco-hysteresis model with these materials during cyclic loading.