A U-tube heat exchanger with integral channel, head and unperforated rim is investigated to establish design rules based on application of elastic plate theory. The effect of tube bending resistance, unperforated rim, channel and head on the rigidity of the tubesheet are considered in the analysis. The solution of the equations for the configurations are presented in compact dimensionless form well suited for detailed parameter study. Numerical results are obtained for typical parameter ranges and some comparisons are made with the well-known TEMA formula. The final design curves and formulas are in a form suitable for consideration as a design code.