Method for smoothing and/or polishing slabs of stone or stone-like material with a machine comprising: a support bench for a slab to be machined resting on a conveyor belt; at least one machining station comprising two bridge support structures (20, 22), transversally arranged astride the support bench, a spindle-carrying beam, suitable for being moved over the bridge support structures along a transverse direction, being provided on said bridge support structures (20, 22); at least one spindle-carrying structure, suitable for being rotated about its own vertical axis, being provided on the spindle-carrying beam; each spindle-carrying structure being provided with two motorized spindles (38A; 38B), the ends of which are provided with machining heads (42A, 42B) arranged spaced apart and opposite each other with respect to the vertical axis of the spindle-carrying structure and comprising machining tools (44A, 44B); a programmable computerized unit for controlling the position, the movement and the speed of the moving members, said method being characterized in that: - the beam and the spindle-carrying structures move coordinated and synchronized with each other; - for each stroke of the beam in the transverse direction, each spindle-carrying structure performs a rotation of 180° about its rotation axis; - when the beam is located at the centre line of the bench, the axis connecting the rotation axes of the spindles (38A, 38B) is perpendicular to the longitudinal direction of the machine; and - when the beam is located at the maximum distance from the centre line of the bench, the axis is parallel to the longitudinal axis of the machine. a support bench for a slab to be machined resting on a conveyor belt; at least one machining station comprising two bridge support structures (20, 22), transversally arranged astride the support bench, a spindle-carrying beam, suitable for being moved over the bridge support structures along a transverse direction, being provided on said bridge support structures (20, 22); at least one spindle-carrying structure, suitable for being rotated about its own vertical axis, being provided on the spindle-carrying beam; each spindle-carrying structure being provided with two motorized spindles (38A; 38B), the ends of which are provided with machining heads (42A, 42B) arranged spaced apart and opposite each other with respect to the vertical axis of the spindle-carrying structure and comprising machining tools (44A, 44B); a programmable computerized unit for controlling the position, the movement and the speed of the moving members, said method being characterized in that: - the beam and the spindle-carrying structures move coordinated and synchronized with each other; - for each stroke of the beam in the transverse direction, each spindle-carrying structure performs a rotation of 180° about its rotation axis; - when the beam is located at the centre line of the bench, the axis connecting the rotation axes of the spindles (38A, 38B) is perpendicular to the longitudinal direction of the machine; and - when the beam is located at the maximum distance from the centre line of the bench, the axis is parallel to the longitudinal axis of the machine. - the beam and the spindle-carrying structures move coordinated and synchronized with each other; - for each stroke of the beam in the transverse direction, each spindle-carrying structure performs a rotation of 180° about its rotation axis; - when the beam is located at the centre line of the bench, the axis connecting the rotation axes of the spindles (38A, 38B) is perpendicular to the longitudinal direction of the machine; and - when the beam is located at the maximum distance from the centre line of the bench, the axis is parallel to the longitudinal axis of the machine.