In this work, the infinitesimal plane analysis of the displacement and stress field of an infinitely large elastic isotropic plate, which has an elliptical stress-free opening, is approximated by the complex stress function. The plate is under a uniform tension at infinity. This problem is solved with given values of the complex stress function on the inner and outer edges, by a conformal mapping of the elliptical domain onto a circle with explicit transformations and with power series expansion of the complex potential.