The invention describes a machine (10) for producing bags of flexible material, comprising a reel-holder group (12) that removably supports at least one reel (14, 16) capable of supplying at least one said flexible material, a welding group (18) provided with at least one upper welding plate (20) and at least one corresponding lower welding plate (22) that are heated and provided with corresponding linear welding tracks, such upper (20) and lower (22) welding plates acting on the film according to a vertical alternate movement, pinching it along one or more linear portions, and at least one cutting group (24, 26) that separates from each other the single bags that have just been obtained further to the welding operation on the film. The lower welding plate (22) is made integral with a base (30), whereas the upper welding plate (20) is mobile with an alternate motion along a plurality of vertical guiding columns (32) and is constrained at the top to a plurality of moving means (36, 38) associated with a cover (40) fixed above such vertical guiding columns (32). Each single moving means (36, 38) is controlled by a respective motor (42) integral with the cover (40).