Under certain exposure conditions, femtosecond lasers create nanogratings in the bulk of fused silica for which the orientation is governed by the laser polarization. Such nanostructure induces stress that affects optical and chemical properties of the material. Here, we present a method based on optical retardance measurement to quantify the stress around laser affected zones. Further, we demonstrate stress dependence on the nanogratings orientation and we show that the stress within single nanogratings lamellae can locally be as high as several gigapascals.