Abstract: For a two-dimensional infinite medium containing an elliptical inclusion of different material, elastic stress distribution formulas are derived. It is pointed out that in the inclusion theory of B.T. Brady there are two errors, namely, (1) the stress component parallel to the minor axis within the elliptical inclusion is not a tensile stress, under far field compression in two directions; (2) shear stress within the inclusion is neither a function of position nor a second order quantity and thus can not be neglected.