Abstract Spherical indentation testing is regarded as an effective technique for deducing the constitutive properties of metallic materials, e.g. the determination of the stress-strain curve (<r-e curve) from the characteristic loadL vs. penetration depth h curve (L-h curve). However, the uniqueness between the L-h curve and the <r-e curve has not systematically addressed yet. The existence of materials having different constitutive laws but visually indistinguishable L-h curves has been probed, thus requiring the development of refined methodologies for distinguishing such materials in the reverse analysis. These topics are deeply discussed in the present paper. The indentation responses of an aluminum alloy (Al 6082-T6) and of a distinct material having apparently indistinguishable L-h curves are examined via a proper experimental characterization and Finite Element Analysis (FEA). For both materials the strain processes occurring in the subsurface region are especially examined and compared. The analysis probes that the actual constitutive properties of the indented material can be distinguished once proper functions accounting for the strain processes promoted by the indenter are formulated. Based on these findings, a suitable L-h curve expression and a new reverse analysis algorithm ensuring the one-to-one correspondence between the L-h curve and the <r-e curve of the indented materials are proposed.