The stress analysis method for fixed tubesheet (TS) heat exchangers (HEX) in pressure vessel codes such as ASME VIII-1, EN13445, and GB151 is based on the classical theory of thin plate on elastic foundation. In addition, these codes all assume a geometric and loading plane of symmetry at the midway between the two TSs so that only half of the unit or one TS is needed to be considered. In this study, a refined general theory of stress analysis for TS is presented which also considers unequal thickness for two TSs, different edge conditions, pressure drop and deadweight on two TSs, the anisotropic behavior of the TS in thickness direction, and transverse shear deformation in TS. Analysis shows floating and U-tube heat exchangers are the two special cases of the refined theory. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the refined theory. Numerical comparison results indicate that predictions given by the refined theory agree well with finite element analysis (FEA) for both thin and thick TS heat exchangers, while ASME results are not accurate or not correct. Therefore, it is concluded that the presented refined general theory provides a single unified method, dealing with both thin and thick TSs for different type (U type, floating, and fixed) HEXs in equal detail, with confidence to predict design stresses.