The invention relates to a process and a device for producing a contour of a planiform piece, intended, in particular, for the internal trim of motor vehicles, in which said piece (1) is cut to define at least an apex (2) of said contour (3), having a given profile P, and a side (4), or so-called first side, of said contour (3) extending from said apex (2). According to the invention, there are carried out sequentially: on one hand, cutting of said piece (1) to produce simultaneously at least said apex (2), according to said profile P, and to cut said first side (4) over a portion, referred to as a fraction F, of its length extending from said apex (2); on the other hand, at least another operation of cutting said piece (1) to produce said first side (4), including at least a portion at least of said fraction F.