Abstract: A flexible coupling has at least one and more commonly a plurality of diaphragms having a particular profile. The profile has first and second contoured sections. The first contoured section has a radially-inwardly decreasing thickness and extends to near the center of the diaphragm and the second section extends therefrom and has a radially-inwardly increasing thickness such that the bending moment developed by axial deflections is small near the thinnest section or the center of the diaphragm, and the stress levels are minimized throughout the diaphragm. The diaphragm profile as described is analytically optimized to tolerate greater axial deflection and bending before the fatigue and endurance limits of the diaphragm material are reached than has heretofore been the case.