Flax (Linum usitatissimum L.) phloem fibers produce a tertiary cell wall as part of regular plant growth. The fiber tertiary cell wall is responsible for supporting the stem’s vertical position and is involved in the implementation of the negative gravitropic reaction when it is tilted. Rhamnogalacturonan I (RG-I) is one of the main matrix polysaccharides of the tertiary cell wall, playing an essential role in its functioning. The distribution of RG-I in fibers isolated from two stem sides (pulling and opposite) during graviresponse was studied. The increased content of galactose-containing polymers in the cell walls of fibers from the pulling stem sides was demonstrated. Differences in the distribution of RG-I epitopes on different sides of the stem were shown. RG-I with branched galactan side chains was found in the fiber tertiary cell walls; the labeling of such side chains in the cell wall of fibers from the pulling side of the stem was increased during gravistimulation. Using transcriptome analysis, the upregulation of genes encoding enzymes involved in RG-I metabolism (synthesis and modifications) in the fibers from the pulling stem side, mainly at the early stage of graviresponse, was revealed. A special role for fasciclin-like arabinogalactan proteins in response to mechanical stimuli was proposed. For the purpose of further modifying the plant cell wall properties, it would be worthwhile to have an understanding of the processes taking place in the fiber cell wall, both in normal conditions and during mechanical stress.