The rewinding machine includes a first winding cradle formed between a first winding roller, a second winding roller and a third winding roller. The first winding roller and the second winding roller define a nip through which there pass the winding cores with the web material being wound around them. The rewinding machine also includes a feed path of the winding cores that pass between the first winding roller and the third winding roller. A second winding cradle is formed between the first winding roller, the second winding roller and a fourth winding roller. The rewinding machine also includes a rolling surface extending around the first winding roller and defining a feed channel of the winding cores.