This paper employ an analytical approach for solving the two-dimensional problems of elasticity and thermo-elasticity in terms of stresses in an inhomogeneous strip which is infinite. We consider application of direct integration method in a plane steady state heat conduction problem for a semi plane. Application of this method are depend on the direct integration of equilibrium equation for efficient analysis of inhomogeneous solids. With the application of direct integration method for differential and compatibility equation for isotropic material, we are reducing desired equation to integro-differential equation. We have solved these dominant equations by applying simple iteration method.The results for displacement and stresses are computed numerically. One can find the displacement in terms of strains by the integration of Cauchy relations. Using Simple iteration method to find thermal stresses in terms of Volterra- integro differential equations.The calculation to construct the solution can be also useful to solve some optimization problem as well as inverse thermoelasticity problems in terms of stresses.