Although the application and development of continuum approaches demonstrate immense promise to model granular flows, the assumption of isotropic stress state in a constitutive law needs to be carefully examined, especially for accurately modeling the kinematics and kinetics of obstructed granular flows. This paper investigates the effect of obstacles on granular stresses and stress ratios in 3D granular silo flows by using discrete element method (DEM). The adopted obstacles include a conical insert, disk insert, BINSERT, hollow cylinder insert and hollow silo insert, as well as the absence of any insert for comparison. A novel (simple but robust) method with ring measurement cells was proposed to determine average stress tensors for granular flows. An innovative slice method with null friction boundaries was also proposed to significantly reduce DEM computational time. The validity of the proposed DEM model was justified by a repose angle experiment and two numerical verification examples. Results reveal that the blocking effect from the obstacles and the hopper wall of the silos led to a significant increase in normal and shear stresses. The normal stresses exhibited slight anisotropy in steady and uniform granular flows, and resulted in a stress ratio of approximately 1.0, indicating an approximately isotropic stress state. Unlike the normal stresses, the shear stresses however showed strong anisotropy even in the steady and uniform regime. The obstructed granular silo flows exhibited strong anisotropy not only in normal stresses, but also in shear stresses. The stress ratio in the obstructed granular flows can appreciably deviate from unity, varying between 0.27 and 2.24. Moreover, the vertical stresses dominated the contact force transmission in the granular silo flows, and showed the formation of dynamic granular arching.