Radial and vertical profiles are determined for a sample of 34 edge-on disk galaxies in the HDFs, selected for their apparent diameter larger than 1.3″ and their unperturbed morphology. The thickness and flatness of their galactic disks are determined and discussed with regard to evolution with redshift. We find that sub-L* spiral galaxies with z ∼ 1 have a relative thickness or flatness (characterized by h_z/h the scaleheight to scalelength ratio) globally similar to those in the local Universe. A slight trend is however apparent, with the h_z/h flatness ratio larger by a factor of ∼1.5 in distant galaxies if compared to local samples. In absolute value, the disks are smaller than in present-day galaxies. About half of the z ∼ 1 spiral disks show a non-exponential surface brightness distribution.