Curves are given which enable the flexibilities and the maximum longitudinal and circumferential elastic stresses to be obtained for thin smooth circular, unpressurised pipe bends having fully rigid flanges at each end, when subjected to pure opening or closing bending moments in the plane of the bend. The curves are based on small deflection, elastic, thin shell theory which assumes the pipe bore radius to thickness ratio is greater than or equal to 10. The stresses are given at various points around the pipe bore at the centre and ends of the bend arc for pipe bend radius to pipe bore radius ratios of 2, 5 and 10.