Tube sheets of U-tube and bayonet-tube exchangers differ from those of floating-head exchangers in that they receive no external support from the staying or column action of the tubes. The strengthening effect of tube-bending reaction is here investigated, evaluated quantitatively, and presented in the form of simple design factors. These factors are functions of a parameter ua , a measure of the relative “barreling” rigidity of the tube bundle as compared to the flexural rigidity of the tube sheet. With stiff tubes and flexible tube sheets (high ua ) the reinforcement due to tube bending is considerable and, in the central region of the tube sheet, the deflection and curvature are essentially independent of any tube-sheet property. At low ua the benefit gained is negligible.