For heat-setting tubular articles (such as can bodies) of an at least partly biaxially oriented crystallizable polymer, preferably a saturated linear polyester such as polyethylene terephthalate, e.g. for thermally processable food containers, a tube of the polymer is fitted over a mandrel and clamped at its ends to the mandrel at a temperature below the glass transition temperature of the polymer. The tube is then heated, e.g. by inserting a heater 28 into the interior of the mandrel, above the temperature to which it is to be heat-set (at least 60.degree. C. above for PET) whereupon it shrinks into contact with the mandrel but is restrained from axial or further radial shrinkage. The tube and mandrel are cooled to below the heat-set temperature and the tube may then be cut into can body sections by knives engaging in circumferential grooves. Contact between the tube and mandrel is released, e.g. by forcing compressed air out through small holes in the mandrel surface to allow the tube and mandrel to be separated. Tubular bodies with one closed end can be heat-set on a mandrel with a correspondingly shaped end.