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Several case history failures of slope systems have highlighted that the instability onset in loose materials can be triggered under prevailed drained conditions and stress paths that can be represented by constant shear drained (CSD) loading. This study uses the anisotropic critical state theory (ACST) to assess the effect of fabric anisotropy and loading characteristics (e.g., Lode angle and principal stress direction) on the instability onset under CSD stress paths, comparing our numerical-based observations with available experimental information. Towards this end, the ACST-based SANISAND-F model’s performance under CSD stress paths is also assessed. In addition, multiaxial conditions are incorporated through the estimation of instability surfaces. The numerical simulations are useful in explaining that the instability onset under CSD loading is dictated by a trade-off of volumetric strain components. Moreover, the results show an important effect of fabric anisotropy on the instability stress ratio (𝜂𝑓 ). For conditions representative of common experimental setups, 𝜂𝑓 decreases with the increase of the Lode angle and the major principal stress inclination, and 𝜂𝑓 increases with the increase of initial fabric intensity, consistent with available experimental evidence. However, these trends can change based on the interaction between the Lode angle and loading/fabric directions; hence, departing from typical experimental observations. Finally, we discuss the potential of a simplified approach to estimate 𝜂𝑓 analytically, including fabric effects.