The rewinding machine includes a path for insertion of tubular cores; a winding cradle; a first moving member designed to be in contact with the web material to be wound; a rolling surface forming, with the first moving member, a channel for passage of the tubular cores; and an insertion device to insert the cores in the channel. At the inlet of the insertion channel there is a second moving member, opposed to the first moving member, the core insertion path passing between the first and the second moving members. The two moving members are arranged at a distance such that a core inserted between them is in contact with the second moving member and with the web material entrained around the first moving member.