In this work material parameters of cyclic plasticity for soft copper and CuCrZr alloy were determined using the combined non-linear isotropic and kinematic hardening law (the Frederick-Armstrong-Chaboche model) for the temperature range between 20 °C and 550 °C. These parameters are the initial kinematic hardening modulus, the rate of change of kinematic hardening modulus, the maximum change in the size of the yield surface and the rate of change of the yield surface size. Both precipitation-hardened and annealing-softened states were examined for CuCrZr alloy. A series of strain-controlled cyclic tensioncompression tests were conducted at four temperature levels. The parameters were calibrated with the stabilised loops of stress-strain curves. The predicted stabilised loops from FEM simulation with the calibrated parameters showed good agreement with the experimental result demonstrating the validity of the considered constitutive model.