A flexible package-forming machine for horizontal packaging by means of folding and welding a flexible band comprising, in this order with respect to a forward movement direction of the flexible band, at least: • one unwinding unit for unwinding a flexible band in the forward movement direction; • one folding unit of a flexible band configured for folding said flexible band along at least one folding line parallel to the forward movement direction, at least two portions arranged on opposite sides of said at least one folding line of one and the same face of the flexible band being arranged opposite one another; • one welding unit of the folded flexible band configured for making welding lines at least in a direction transverse to the forward movement direction of the flexible band; • one cutting unit for cutting the folded flexible band to separate the portions making up the flexible packages; and wherein the forming machine further includes at least one drive unit configured for moving the flexible band in the forward movement direction; characterized in that the cutting unit is a laser cutting unit provided for making cuts in a cutting area of the folded flexible band, separating each individual flexible package from the flexible band and providing a fill opening in each flexible package by means of at least one fill opening cut, said cutting unit at least being provided with: • at least one emitting unit for emitting laser light located on one side of the folded flexible band; • a directional device for directing the laser light against a cutting area of said folded and welded flexible band; • at least one immobilizing clip configured for pressing along a portion of the folded flexible band adjacent to the cutting area for the immobilization thereof; • a separator device including an insertable separator element interposed between the opposite faces of the folded flexible band, in an area adjacent to the fill opening, for separating the opposite faces of the flexible band during cutting operations to prevent the fusion thereof; wherein said separator element is movable in a vertical direction not parallel to the forward movement direction of the flexible band between an inserted position in which the separator element is inserted between the opposite faces of the folded flexible band through edges of the flexible band farthest away from the folding line up to a position adjacent to the cutting area of the fill opening cut, and an extracted position in which the separator element does not interfere with the welding lines of the flexible band in the movement thereof in the forward movement direction. • one unwinding unit for unwinding a flexible band in the forward movement direction; • one folding unit of a flexible band configured for folding said flexible band along at least one folding line parallel to the forward movement direction, at least two portions arranged on opposite sides of said at least one folding line of one and the same face of the flexible band being arranged opposite one another; • one welding unit of the folded flexible band configured for making welding lines at least in a direction transverse to the forward movement direction of the flexible band; • one cutting unit for cutting the folded flexible band to separate the portions making up the flexible packages; • at least one emitting unit for emitting laser light located on one side of the folded flexible band; • a directional device for directing the laser light against a cutting area of said folded and welded flexible band; • at least one immobilizing clip configured for pressing along a portion of the folded flexible band adjacent to the cutting area for the immobilization thereof; • a separator device including an insertable separator element interposed between the opposite faces of the folded flexible band, in an area adjacent to the fill opening, for separating the opposite faces of the flexible band during cutting operations to prevent the fusion thereof;