Abstract An interpretation of spherical indentation experiments and the determination of hardening law parameters is the challenge in this paper. A new protocol based on multiple cyclic loading allowed models describing the indentation data changes to be determined from a numerical study. Inversion of these models, determined for two constitutive equations with isotropic hardening, combined with a sensitivity study enabled the study of the uniqueness of the solution. It is shown that although the new protocol is not necessary to determine the two Hollomon equation parameters, it is necessary to determine accurate values of the three Ludwig equation parameters. From an experimental study, it was shown that methods based on a “reverse” analysis can be used in order to have an evaluation of the mechanical properties in a first-order approximation.