A solution of the plane strain deformation of a two layered Earth model consisting of a homogeneous, elastically isotropic layer (EIL) of finite thickness lying on a homogeneous, elastically isotropic half-space (EIHS) induced by two-dimensional faulting placed in the EIHS is obtained. The Airy’s stress function method is used to obtain the deformation field in the integral form induced by a blind dip-slip faulting. The linear combination of exponential terms occurring in the denominator of integral expressions is estimated as a finite sum of exponential terms (FSET) employing least square method. Then the integrals are evaluated analytically. The displacement field is computed analytically and numerically for two different models of Earth. The stresses can be computed similarly