Wrapping granular soils in geosynthetic containers, such as soilbags, results in a considerable increase in the bearing capacity due to the effective restraint on the dilatancy of the soil. This paper numerically investigates the stress states and fabric anisotropies in the wrapped soil using the discrete element method, providing a novel perspective for new insights into the reinforcement mechanisms and the development of constitutive relations for soilbags. The two most anticipated loading conditions, namely, unconfined compression and simple shear, are considered, and numerical predictions are compared to experimental results. During unconfined compression, both global and local p–q stress paths evolve linearly, having the same slope until the global failure of the wrapping geosynthetic. Under simple shear, the global stress path approaches the critical state line first and then turns to the compression line of the wrapped soil. Some local loading–unloading stress paths are observed, which may account for the high damping of soilbags during cyclic shear. The reduced fabric anisotropies of the normal and tangential force chains suggest greater confinement from the lateral sides of the geosynthetic container in either loading course. The performance and mechanisms of the soilbag earth reinforcement method, i.e., confinement and interlocking, can be better understood based on these new findings on the stress states and fabric anisotropies.