A composition for shrinkable film which excels in heat-sealability, transparency, strength, and particularly low-temperature quick shrinking property and, therefore, suits production chiefly of packaging materials, a film made of the composition and a process for the manufacture of the film are disclosed. Specifically, the composition comprises one of the specific combinations of components (A), (B) and (C), i.e. the combinations of (A)+(B), (B)+(C) and (A)+(B)+(C), wherein (A) is non-rigid polyolefine resins such as ethylene vinyl acetate, (B) is an elastomer comprising a specific ethylene-.alpha.-olefin copolymer, and (C) is rigid polyolefin resins such as polypropylene. The packaging film excelling particularly in optical property, mechanical strength and low-temperature shrinking property is obtained by converting a homogeneous blend of the aforementioned composition, either in its crosslinked form or in its non-crosslinked form, into a tubular raw film, which is stretched at a temperature low enough for imparting a high orientation to the film. The process for the manufacture of this packaging film is also disclosed.