The effect of the precipitation-bath concentration on the viscoelastic properties of wet-spun polyacrylonitrile fiber was studied. The polymer system to be deformed was modeled structurally as a network of intermolecular linkages that consisted of viscous and elastic nodes and could be used to explain many physical phenomena occurring during the deformation, in particular, the known phenomenon of forming voids and vacuoles in the spun fiber. It was shown that the jet-fiber during spinning into mild baths transitioned sequentially from the viscoelastic state, initiating a pathway that formed a viscous (Newtonian) state at its end. The effect of the precipitant composition on the structure-fixation length and time for a jet in the viscous and viscoelastic states was examined.