A flexographic printing unit, for a sheet along a printing line, comprising - a plurality of printing assemblies, each comprising a printing roller apt to include a printing block, - automatic, programmable displacement means for said printing rollers, apt to distance at least one of said printing rollers 22 from said printing line during the printing process, so that said printing roller does not print said sheet, - each of said printing assemblies comprising: - a structure fixed to the floor, - at least one frame, which is movable with respect to said structure fixed to the floor, comprising said at least one printing roller and apt to be moved by said displacement means, - and said printing unit being characterized in that each of said printing assemblies further comprises - damping means arranged between said frame and a fixed point so as to damp and facilitate and push the movement of said frame comprising a pneumatic cylinder and a storage tank external to said unit and in fluid passage connection with said pneumatic cylinder so that, when said pneumatic cylinder is deformed, the variation in overall volume of said damping means including the pneumatic fluid is less than 20% and that said damping means make a passive actuator when they push the movement of said frame. - a plurality of printing assemblies, each comprising a printing roller apt to include a printing block, - automatic, programmable displacement means for said printing rollers, apt to distance at least one of said printing rollers 22 from said printing line during the printing process, so that said printing roller does not print said sheet, - each of said printing assemblies comprising: - a structure fixed to the floor, - at least one frame, which is movable with respect to said structure fixed to the floor, comprising said at least one printing roller and apt to be moved by said displacement means, - and said printing unit being characterized in that each of said printing assemblies further comprises - damping means arranged between said frame and a fixed point so as to damp and facilitate and push the movement of said frame comprising a pneumatic cylinder and a storage tank external to said unit and in fluid passage connection with said pneumatic cylinder so that, when said pneumatic cylinder is deformed, the variation in overall volume of said damping means including the pneumatic fluid is less than 20% and that said damping means make a passive actuator when they push the movement of said frame. - a structure fixed to the floor, - at least one frame, which is movable with respect to said structure fixed to the floor, comprising said at least one printing roller and apt to be moved by said displacement means, - and said printing unit being characterized in that each of said printing assemblies further comprises - damping means arranged between said frame and a fixed point so as to damp and facilitate and push the movement of said frame comprising a pneumatic cylinder and a storage tank external to said unit and in fluid passage connection with said pneumatic cylinder so that, when said pneumatic cylinder is deformed, the variation in overall volume of said damping means including the pneumatic fluid is less than 20% and that said damping means make a passive actuator when they push the movement of said frame.