An extrusion apparatus intended for producing a continuous strip of profiled product (P) comprising a screw (2) rotating in a fixed body (1) comprising a supply inlet (3) for elastomer mixture and an outlet (4) provided with an extrusion nozzle (5) that discharges into the gap formed between a first roller (6) and a second roller (7) that rotate in opposing directions of rotation, the apparatus comprising first means for rotating the first roller (6) and first control means capable of synchronising the speed of rotation (Ω r1 ) of the first roller (6) and the speed of rotation (Ω vis) of the screw (2), and second means for rotating the second roller (7) at a different speed of rotation (Ω r2) than the speed of rotation of the first roller (Ω r1). According to the invention, said first control means are connected to the means for driving the screw so as to adjust the speed of rotation of the screw (2) based on the width of the strip of profiled product (P) and it comprises second control means connected to said second means for rotating, so as to adjust the speed of rotation (Ω r2) of the second roller (7) based on the thickness of said strip.