  We studied a sample of 58 edge-on spiral galaxies at redshifts $z \sim 1$
selected in the Hubble Ultra Deep Field. For all galaxies we analyzed the 2D
brightness distributions in the $V_{606}$ and $i_{775}$ filters and measured
the radial ($h_r$) and vertical ($h_z$) exponential scales of the brightness
distribution. We obtained evidence that the relative thickness of the disks of
distant galaxies, i.e., the ratio of the vertical scale height and radial scale
length ($h_z/h_r$), on average, exceeds the relative thickness of the disks of
nearby spiral galaxies. The vertical scale height $h_z$ of the stellar disks of
galaxies shows no big changes at $z \leq 1$. The possibility of the evolution
of the radial scale length $h_r$ for the brightness distribution with redshift
is discussed.
