The problem of embedded flat elliptical crack in an infinite linear elastic solid is investigated to obtain the displacement field of the crack-face. The solid is considered to be under mode I remote tension. This can be modelled as a complementary problem subjected to pressure on the crack-face, which can be assumed as an arbitrary normal traction expressed in a polynomial form on the crack-face. Trefftz’s potential formulation is used as the foundation of the present paper to evaluate the crack-face displacement field. The displacement and stresses can be obtained in terms of the partial derivatives of the aforementioned potential functions. The displacement field solution is plotted in MATLAB for uniform pressure loading on the face of embedded elliptical crack for specific values of the major and minor axes of the elliptic crack.