An olefin/aromatic vinyl compound copolymer which is excellent in transparency and which satisfies flexibility and heat resistance simultaneously can be produced by carrying out polymerization in such a manner that at least one of conditions: (a) the polymerization is carried out to an aromatic vinyl compound monomer conversion ratio of at least 50 mol % when the polymerization is completed, and (b) the polymer concentration is at least 10 mass % relative to the polymerization solution when the polymerization is completed, is satisfied, and the olefin partial pressure is changed so that the olefin partial pressure when the polymerization is completed is from 1.3 to 20 times the olefin partial pressure at the initiation of the polymerization.