Thin shell theory is applied to pipe bends terminated by flanges or flange-ended tangent pipes and subjected to any end loading, either in-plane or out-of-plane. Graphs of flexibility factor versus pipe bend characteristic are presented for in-plane bending of a wide range of pipe elbows terminated by flanges or short flange-ended tangents. Experimental results verify the thin shell solutions for in-plane and out-of-plane bending of a flanged pipe elbow. The capabilities of a computer program BENDPAC are also described.