Ti2AlNb intermetallic alloy is a relatively newly developed high-temperature-resistant structural material, which is expected to replace nickel-based super alloys for thermally and mechanically stressed components in aeronautic and automotive engines due to its excellent mechanical properties and high strength retention at elevated temperature. The aim of this work is to present a fast and reliable methodology of inverse identification of constitutive model parameters directly from cutting experiments. FE-machining simulations implemented with a modified Johnson-Cook (TANH) constitutive model are performed to establish the robust link between observables and constitutive parameters. A series of orthogonal cutting experiments with varied cutting parameters is carried out to allow an exact comparison to the 2D FE-simulations. A cooperative particle swarm optimization algorithm is developed and implemented into the Matlab programs to identify the enormous constitutive parameters. Results show that the simulation observables (i.e., cutting forces, chip morphologies, cutting temperature) implemented with the identified optimal material constants have high consistency with those obtained from experiments, which illustrates that the FE-machining models using the identified parameters obtained from the proposed methodology could be predicted in a close agreement to the experiments. Considering the wide range of the applied unknown parameters number, the proposed inverse methodology of identifying constitutive equations shows excellent prospect, and it can be used for other newly developed metal materials. (C) 2018 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd.