A film or tube of a specific copolymer of ethylene with 3.0 to 18.0 mole % of a comonomer containing a polar functional group, for example, vinyl acetate is treated with a sulfonating agent at a lower temperature for a short time to give a hydrophilic membrane excellent in hydrophilic properties as well as other properties such as folding endurance or alkali resistance. The hydrophilic membrane is useful as ion-exchange membrane, separator for storage battery or dialysis diaphragm. It is also similar to cellophane in transparency as well as in properties and therefore can be used in, for example, processing of a smoked ham.