The machine (1;100) comprises a winding station (3; 101), adapted to receive secondary winding cores (T) coaxial with, and adjacent to, one another. The machine further comprises a cutting device (11; 104) with a plurality of blades (13; 105), arranged upstream of the winding station (3; 101) with respect to the feeding direction of the web material (N) and adapted to slit the web material into a plurality of strips (S1-S5) of web material. An in-line measurement arrangement (81-87) is also provided for measuring the Poisson's ratio of the web material (N).