Phenomenological constitutive equations contain material parameters which cannot be measured directly in the experiment. We address the problem of error-resistant parameter identification for models of large strain elasto-plasticity. The identification is based on tests with a heterogeneous stress state. A methodology is presented which allows us to assess the reliability of identification strategies in terms of their sensitivity to measurement errors. A vital part of the methodology is the mechanics-based metric in the space of material parameters. The measure of sensitivity is the size of a parameter cloud, computed using this metric. Efficient procedures of Monte Carlo type for computation of the parameter cloud are presented and discussed. The methodology is exemplified in terms of a model with combined nonlinear isotropic-kinematic hardening. First, for an aluminum alloy, non-monotonic torsion tests with different sample cross sections are analyzed. Second, for the identification of hardening parameters of steel, three different tension–compression samples are considered. In both examples, various combinations of tests are checked for sensitivity to measurement errors identifying best and worst combinations.