In this paper we compute elastoplastic properties of hydroxyapatite single crystals from nanoindentation data using a two-step algorithm. In the first step the yield stress is obtained using hardness and Young’s modulus data, followed by the computation of the flow parameters. The computational approach is first validated with data from the existing literature. It is observed that hydroxyapatite single crystals exhibit anisotropic mechanical response with a lower yield stress along the [1010] crystallographic direction compared to the [0001] direction. Both work hardening rate and work hardening exponent are found to be higher for indentation along the [0001] crystallographic direction. The stress–strain curves extracted here could be used for developing constitutive models for hydroxyapatite single crystals.