An assembly of the present invention for a syringe is composed of a barrel, made of cyclic polyolefin, which has a barrel body having a distal end part and a piercing needle which has a piercing needle tip at its distal end and is fixed to a piercing needle fixing portion of the barrel and a seal cap mounted on the barrel. The seal cap is formed of a thermoplastic elastomer composition containing as its main component a mixture of a styrene-based thermoplastic elastomer and a softener, for hydrocarbon-based rubber, which has a kinematic viscosity of 1 to 5,000 mm2s−1 at 100 degrees C. and a naphthenic carbon ratio (% CN) of not more than 20% when said naphthenic carbon ratio is measured by ring analysis.