A polyamine curable, highly saturated nitrile rubber composition comprising 100 parts by weight of a polyamine curable, highly saturated nitrile rubber having an α,β-ethylenically unsaturated nitrile monomer unit, a diene-based monomer unit, an α,β-ethylenically unsaturated dicarboxylic acid monoester monomer unit, and an α,β-ethylenically unsaturated carboxylic acid ester monomer unit other than the α,β-ethylenically unsaturated dicarboxylic acid monoester monomer unit, and having an α,β-ethylenically unsaturated nitrile monomer unit content of 22.0 to 24.5 wt. %, preferably 22.5 to 24.5 wt. %, and an iodine value of 120 or less, and 4 to 31 parts by weight of an aliphatic carboxylic acid diester compound of polyalkylene glycol. The polyamine curable, highly saturated nitrile rubber composition is used as a cure molding material of a sealing material that can be suitably used even in an environment in which the sealing material is exposed to polycyclic aromatic compound.