A process and apparatus for the production of laminated sheath cables having improved close contact between a laminated tape layer and the core of the cable. The tape is longitudinally wrapped around the cable with portions of the tape overlapping. The assembly is then heated and passed through a set of pressing rollers disposed at a single pressing position. The rollers are at least three in number. The arc length of each roller is determined by dividing the total outer circumference of the assembled tape and cable core by the number of rollers.