There are provided a radiation curing silicone rubber composition that is useful for the bonding of substrates, an adhesive silicone elastomer film formed from such a composition, a structural body in which two substrates are bonded via a cured layer formed from the composition, and a method of producing such a structural body. The composition includes: (a) an organohydrogenpolysiloxane containing at least one group selected from the group consisting of acryloyl groups and methacryloyl groups, and at least one hydrosilyl group; (b) a fluid organopolysiloxane with at least two groups which are each selected from the group consisting of acryloyl groups and methacryloyl groups, and with no hydrosilyl groups; (c) a compound selected from the group consisting of alkoxysilanes, partial hydrolysis-condensation products of alkoxysilanes, organosilane-modified isocyanurates and organosiloxane-modified isocyanurates; (d) a radiation sensitizer; and (e) a platinum group metal-based catalyst. The composition is of low elasticity, while also providing excellent heat resistance, adhesion, and workability.