A cross-linked rubber product is obtained by cross-linking an acrylic elastomer composition containing an acrylic elastomer obtained by copolymerization of an acrylate and a cross-linking site monomer. The molar fraction of an oxygen atom (a) in the acrylic elastomer is 11.3 mol % or less, the molar fraction of a nitrogen atom (b) in the acrylic elastomer is 0.5 mol % or less, and a volume change is from −3 to 6% when the cross-linked rubber product is dipped in distilled water at 80° C. for 200 hours.