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The onset of static liquefaction in anisotropically consolidated soils is of relevance in assessing the performance of geotechnical systems. Previous studies have also highlighted the role of inherent soil fabric. This study derives an analytical instability criterion for granular materials under undrained loading by using the relatively new anisotropic critical state theory (ACST). The criterion is established using the SANISAND-F model, and it is amenable to incorporating consolidation anisotropy and fabric effects. We assess different numerical strategies for simulating the instability onset on materials sheared from initially anisotropic conditions. Our assessments indicate that simulations that consider consolidation followed by shear better represent the response observed in laboratory tests. It is observed that the degree of anisotropic consolidation has no significant effect on the instability stress ratio, but a very high degree of anisotropic consolidation results in a spontaneous collapse. It is also observed that the anisotropic consolidated specimens have a higher instability stress ratio in triaxial compression than in triaxial extension, highlighting the effect of loading direction relative to the existing fabric.