In connection with the non-destructive stretching and fastening of pelts (2) on distention elements/pelt boards (4), where the pelt is stretched and fastened in the stretched position during the drying process by means of a fixing bag, it has shown that the pelts give way (shrink) on each side of the tail root of the pelt, with the result that use is made of a number of staples for the fastening of these places on the stretched pelt. Since it is not at all desirable to use staples, a development of the pelt boards (4) has taken place, so that these have an arched extent around two transverse axes in relation to their longitudinal axes. Moreover, it has long been desirable to be able to stretch the pelts to a greater degree, which has not been possible with the use of the known stretching machines. This development has led to the development of a method and a stretching machine for the execution of the method, where the gripping elements are configured to correspond with the shape of the pelt board, and where the pelt is engaged by the gripping elements along the whole of the lower periphery of the pelt, so that the counter-hold force in the pelt is distributed over the whole periphery of the pelt, whereby the pelt can be stretched to a greater degree without any damage to the pelt in the areas of engagement for the gripping elements.