The critical state soil mechanics (CSSM) framework has been widely used across a range of problems in geomechanics involving complex loading conditions. However, the uniqueness of the critical state has been disputed for many years and it remains a controversial issue. Motivated by previous investigations, a series of discrete element method (DEM) simulations were performed under both axial compression (AC) and axial extension (AE) stress paths. All samples were isotropically compressed at varying mean normal effective stresses (confining pressures) and sheared to a large axial strain of approximately 60%. It is found that there exist unique values of critical void ratios and stress ratios under critical state, which are independent of the samples’ initial packings but dependent on stress paths. And the critical strength (stress ratio) for the AC stress path tests is higher than that for the AE stress path. The critical state lines (CSLs) are found to path-dependent but unique for each stress path. A unique linear relationship between the critical coordination numbers and critical void ratios is identified under the AC and AE stress paths respectively, but such a relationship depends on the stress paths. It is also found that there exist unique values of microscopic parameters in terms of deviator fabric under critical state, which are independent of the samples’ initial packings but dependent on stress paths. All these simulation results lead to the conclusion of non-uniqueness of CSLs from both macroscopic and microscopic viewpoints.