Fabrication conditions and material rheology control the process of film blowing and limit the possible shapes the bubble may take as well as the ranges and ratios of stresses within the bubble. In order to understand bounds on the stresses during the blowing process, we explore the constraints imposed by force balances, the thin shell approximation, and thermodynamics. We show that the ratio of axial stress to hoop stress is independent of the explicit terms for film thickness, velocity, heat transfer, and the rheology of the material. In addition, we demonstrate that the ratio of the axial stress to the hoop stress can be calculated at any point in the blown-film requiring only values for the pressure drop across the bubble, the shape of the bubble, and the force pulling up the bubble. Experimental results, as well as certain theoretical evidence, strongly indicate that the ratio of axial to hoop stress is everywhere greater than 1 in the standard blown-film process. If this is generally true, then the stress relations we derived can be employed to test the applicability of various theoretical models of the blown-film process.