The present invention provides a production process of a heat shrinkable film which is transparent, excellent in the balance of physical properties such as rigidity, elongation and shrink properties in both MD and TD, especially has a uniform film thickness and good stability in extrusion molding film while utilizing an inflation method; a block copolymer or hydrogenated product thereof, or a composition composed thereof excellent in tensile properties, optical properties, hardness, stretch properties, molding processability, shrink properties and solvent resistance and therefore suited for extrusion, injection molding and foams. The production process of a heat shrinkable film has a first inflation step of forming a tube having a thickness of from 0.05 to 0.5 mm by using a block copolymer having a vinyl aromatic hydrocarbon content of from 65 to 95 wt. % and a conjugated diene content of from 5 to 35 wt. %, or a hydrogenated product of the block copolymer; and a second inflation step, successively to the first inflation step, stretching the tube to from 1.5 to 5 times the original length in the TD in a fluid of from 65 to 100° C.