A machine for producing paper rolls includes a first and a second winding rollers rotatably mounted, respectively, about first and second axes; first and second pressure rollers rotate, respectively, about a third axis on a first movable arm, and about a fourth axis on a second movable arm. The rollers define a winding channel for a web of paper around a core, for forming a roll. The core moves by one or more of the rollers, between a position for winding and position for expelling the wound roll. The winding rollers are positioned, relative to the pressure rollers on opposite sides of the channel, relative to movement of the core The movable arms pivot, respectively, on first and second secondary axes such that the rotation of the first and/or the second movable arm moves the first and/or the second pressure roller from or towards the first and/or second winding roller.