The invention is directed to a method of extracting polysaccharides from alfalfa plants, the method comprising the followings steps: milling of the alfalfa plants; addition of a buffer solution to the milled alfalfa plants and separation of said milled plants, thus producing a polysaccharides-composed supernatant and a protein- composed pellet; and precipitation of the polysaccharides in the polysaccharides-composed supernatant; the alfalfa plants comprising alfalfa seeds; and the method comprising the following steps, prior to the milling step: soaking of the alfalfa plants in water so as to swell the alfalfa seeds; mesh filtration of the alfalfa plants comprising the swollen alfalfa seeds; and drying of the alfalfa plants comprising the swollen alfalfa seeds.