We present a study of the filamentary structure in the neutral atomic hydrogen (H I) emission at the 21 cm wavelength toward the Galactic plane using the 16′.2-resolution observations in the H I 4π (HI4PI) survey. Using the Hessian matrix method across radial velocity channels, we identified the filamentary structures and quantified their orientations using circular statistics. We found that the regions of the Milky Way’s disk beyond 10 kpc and up to roughly 18 kpc from the Galactic center display H I filamentary structures predominantly parallel to the Galactic plane. For regions at lower Galactocentric radii, we found that the H I filaments are mostly perpendicular or do not have a preferred orientation with respect to the Galactic plane. We interpret these results as the imprint of supernova feedback in the inner Galaxy and Galactic rotation and shear in the outer Milky Way. We found that the H I filamentary structures follow the Galactic warp and flaring and that they highlight some of the variations interpreted as the effect of the gravitational interaction with satellite galaxies. In addition, the mean scale height of the filamentary structures is lower than that sampled by the bulk of the H I emission, thus indicating that the cold and warm atomic hydrogen phases have different scale heights in the outer galaxy. Finally, we found that the fraction of the column density in H I filaments is almost constant up to approximately 18 kpc from the Galactic center. This is possibly a result of the roughly constant ratio between the cold and warm atomic hydrogen phases inferred from the H I absorption studies. Our results indicate that the H I filamentary structures provide insight into the dynamical processes shaping the Galactic disk. Their orientations record how and where the stellar energy input, the Galactic fountain process, the cosmic ray diffusion, and the gas accretion have molded the diffuse interstellar medium in the Galactic plane.