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This paper deals with the determination of the stress distribution at the fillet of a ANSI B16.5 flanges attached internally to a hollow cylinder. A load parallel to the axis of the cylinder and of variable eccentricity acts on a bearing plate which rests on the flange. The strains are measured by means of electrical resistance wire strain gages. The ratios of the mean cylinder diameter to the cylinder wall thickness and of the mean cylinder diameter to the flange thickness are varied. The principal stresses at the fillet are given as functions of these parameters. The experimental results are compared with the stresses calculated on the basis of an approximate theoretical solution for both an axial and an eccentric load.