A process is provided for removing sulfur oxides from gaseous mixtures such as flue gases or tail gases. The process involves contacting the gaseous mixture with a non-functionalized polymeric sorbent which is essentially hydrophobic, such as styrenic polymers. The process may utilize pressure swing adsorption techniques, and is capable of producing a desorption stream with an SO.sub.2 concentration suitable for immediate conversion to elemental sulfur by the Claus process.