An SZ laying machine for umbilical/power umbilical is described. Starting from an input end the machine includes: a first die receiving and collecting a first set of elongate elements substantially rectilinear from respective supplies of elongate elements, a second static die which receives and collects a second set of elongate elements substantially rectilinear from respective supplies of elongate elements and this second set is closed together with the first set into an assembled bundle, at least one supporting means which keeps the assembled bundle radially in place; a revolving device able to torsional rotate the bundle back and forth in an oscillating SZ manner, and a tape or band winding apparatus which in immediate proximity to the revolving device applies band or tape circumferentially onto the SZ laid bundle of elongate elements.