When strength of a structure is discussed, amount of stress and strain concentration at discontinuous portion would be considered as one of the most important factors. As an example, strict stress analysis around an elliptical portion of different material and different thickness in infinite plate has been carried out. The problem of an elliptical boundary is a simple one. In this analysis, however, boundary conditions required for continuity in displacements and stresses are all satisfied. Therefore, some additional methods to usual analytical way have to be used. As for more complicated boundaries and loading conditions, this analytical way would be similarly applied.