Process for sewing and folding a flexible work piece

A process of covering an object with a flexible cover, said object having a front side to be covered and comprising in combination cutting out a flexible piece (25) having a shape corresponding to that of the front side of the object and an additional border (25a) along its contour, stitching into said border (25a) at the edge of the piece at least one auxiliary thread (4) in such a manner as to form an overcast at the edge of the piece for providing an overcast passage extending along said border and placing a tensioning thread (5) in said overcast passage between a stitching line (Pq) of the auxiliary threads in the material and an outer line (Pa) hooking up the threads to each other in such a manner that the tensioning thread can slide within and along said passage with thread lengths projecting at both ends (5a, 5b), covering the front face of the object with the piece in such a manner that the border provided with the tensioning thread extends beyond the object contour, folding back said border at the edge of the object and applying tension to the two ends (5a, 5b) of the tensioning thread to shorten the length of the tensioning thread within said passage and to tighten and fold said border, and locking the ends of the tensioning thread after tension is applied.