A polyethylene film composition characterized as having a broad molecular weight distribution, Mw/Mm 15, a density of 0.920 to 0.970 g/cc, a melt flow index (190.degree. C./2.16 kg) of 0.01 to 0.2 g/10 min., the polyethylene film composition being produced by melt extruding a linear copolymer at a temperature of at least 180.degree. C. in the presence of an amount of a free radical initiator sufficient to improve bubble stability without any significant reduction in the tear strength of film produced from the composition as compared with film produced from the linear copolymer that has not been treated with the free radical initiator.