The invention relates to the method of the preparation of polysaccharide fibers based on hyaluronic acid, a compound comprising hyaluronic acid and metal ions, schizophylan, chitin/chitosan-glucan complex, a compound comprising chitin/chitosan-glucan complex and metal ions, internal mixture of chitin and chitosan, a compound comprising internal mixture of chitin and metal ions, sodium alginate, potassium alginate, ammonium alginate, xanthane, xanthane sodium salt, xanthane potassium salt, oxycellulose, oxycellulose sodium salt, oxycellulose potassium salt, carboxymethyl cellulose, carboxymethyl cellulose sodium salt, and carboxymethyl cellulose potassium salt, or a mixture of polysaccharides, in a non-stationary coagulation bath. Further the invention relates to covers of internal and external wounds and skin defects based on these fibers, and a method of production thereof, and the apparatus for the preparation of polysaccharide fibers.