The influence of the grain orientation on the long-range internal stress associated with the accumulation of geometrically necessary dislocations (GNDs) during plastic deformation is numerically investigated. GNDs stored at grain boundaries (GBs) do not systematically generate a backstress inside grains. Surprisingly, long-range anti-backstress promoting dislocation dynamics and plastic strain inside grains arises at certain GBs interfaces from the accumulation of GNDs. This discovery on one important elementary mechanism affecting the macroscopic mechanical behavior of polycrystals provides guidelines to improve the physical content of current crystal plasticity models.