This article presents an assessment of the yield criterion for porous plastic single crystal, proposed by Paux et al. (2015), for face-centred cubic and hexagonal close-packed crystalline structures. Comparisons with reference FFT full-field computations on single voided cubic unit cells, presenting different crystal orientations, show an overall agreement for the different plastic anisotropies considered at low and high triaxiality. An extension of the criterion to hardenable crystals, which takes into account the spatial heterogeneity of the approximate plastic strain field, is further proposed and compared with FE results from the literature for body-centred cubic crystals.