Abstract In this paper, the Discrete Element Method (DEM) is employed to numerically explore the response of hollow cylinder specimens of granular soils under complex stress paths. Two series of numerical tests are conducted to clarify the effects of the principal stress direction α and the intermediate principal stress through the b-value on the mechanical response of granular materials. The effects of α and b-value on the non-coaxiality of the principal stress and the principal plastic strain increment directions are investigated. It is observed that b-value and α significantly affect the non-coaxial behavior of granular materials. Finally, the results are discussed and compared with those obtained from physical laboratory tests.