The adsorption of Cu(II), Ni(II), Zn(II), and Pb(II) from aqueous solutions on acrylonitrile copolymer sorbents was studied. We prepared five types of sorbents from polyacrylonitrile by varying its concentration in the initial polymer solution and the composition of the coagulation bath, aiming to achieve a different porous structure, The specific area, pore volume, and pore radius of the sorbents were determined on a porosimeter. The porous structure was studied by scanning electron microscopy. Modification of sorbents with sodium hydroxide and hydroxylamine was carried out to form amidooxyme and carboxylic groups with proven complex-forming properties toward heavy metal ions. The optimal pH of the sorption of metal ions was found. The adsorption kinetics were investigated. The order of polymer sorbents toward the sorption of Pb(II), Cu(II), Ni(II), and Zn(II) ions, and the order of heavy metal uptake were determined for all types of sorbents. The effectiveness of heavy metal desorption and the coefficient of recovery of sorption ability were determined.