To realize the sure stretching of a material web with a simple constitution easily actionably without any strain.

A stretching device equipped with tentering rolls for smoothing a material web 7 has two rotatable roll bodies 1 and 2. Each of both the roll bodies 1 and 2 is formed into a truncated cone. In addition, the larger diametral side of each of the roll bodies 1 and 2 faces towards the outside of the material web 7. Both these roll bodies 1 and 2 are supported on rotating shaft lines 3 and 4, which respectively and includedly extend outwards and make an obtuse angle at the middle point of the material web 7.