A method of chemically stabilizing multivalent oxyanions in residue materials such as wastes from glass manufacturing facilities which method involves adding to the residue material cement, lime and aluminum sulfate to form a clay-like material having a low leachability and permeability to water. Calcium polysulfide or other sulfide bearing materials can also be added to assist in stabilizing multivalent oxyanions by adjusting the oxidation-reduction potential of the stabilized waste matrix.