© 2019 Elsevier Ltd This paper concerns the use of (load-displacement) data obtained during spherical indentation of a superelastic (NiTi) alloy, so as to obtain a stress-strain curve. The methodology, which is already starting to become established for conventional plasticity, involves iterative FEM simulation of the indentation process, aiming to optimize agreement between modeled and measured outcomes (load-displacement plots in this case), by systematically varying the values of the parameters in a constitutive law. This worked well for the loading part of the stress-strain curve, but much more poorly for the unloading part. This inaccuracy is attributed to limitations in the standard representation (as implemented via the UMAT routine in ABAQUS) of the unloading part of the loop. A simple analytical formulation is proposed that might be suitable for future use in FEM software for simulation of superelastic deformation.