To obtain a resin for injection molding a cap, capable of injection- molding a cap, especially a tear-off cap, more excellent in easy tear-off property, resistance to crack by environmental stress, and impact resistance at a low temp. than conventional injection-molded caps.

This resin capable of injection-molding a cap is a copolymer comprising ethylene and a 3-12C α-olefin using a single site olefin polymerization catalyst and has a limiting viscosity measured in decalin at 135°C of 0.5-2.5 dl/g, a ratio [gη*] to the limiting viscosity of a linear ethylene-propylene copolymer having the same weight average mol.wt. (by light scattering method) and contg. 70 mol% ethylene in the range of 0.2-0.95, and a 50% crack generation time of not shorter than 50 hr. It is pref. that the copolymer is capable of injection-molding a tear-off cap having a tear-off strength in the range of 100-200 kg/cm2.