We analyze different strategies used for the identification of material parameters, which appear in a certain model of finite strain viscoplasticity. The main focus is set on the sensitivity of the parameters with respect to measurement errors. In different strategies we combine experimental data obtained from various torsion tests with a heterogeneous stress state. A direct problem is solved using the nonlinear FEM. To estimate the stability of a certain identification strategy we perform Monte Carlo simulations for a series of noisy experimental data. A distance between two sets of material parameters is measured using a special mechanics-based metric. Both the identification of material parameters and the estimation of their stability are illustrated by an example. In this example we employ a set of synthetic experimental data obtained for the steel 42CrMo4. As a material model, we choose a model of finite strain plasticity with a combined isotropic-kinematic hardening.