Abstarct: One of the important issues in the design of advanced engineering structures is the prevention of failure of structures due to tension in the geometric discontinuities. Stress concentration causes a recession of strength and premature failure in the structures because it causes the crack progress due to thermal loading and plastic deformation at the location of stress concentration. One of the influential parameters in the distribution of stress around the inclusion is the type of geometry of the inclusion. The amount and location of stress are changed by changing the geometry of the inclusion. In addition to the inclusion geometry, other effective parameters include the rotation angle of the inclusion and the radius of curvature of the inclusion corners (bluntness parameter). By choosing each of these parameters, the maximum stress can be controlled. baxsed on the theory of the two-dimensional thermoelasticity, the stress field around the inclusion is investigated in an infinite isotropic plate. The infinite plate is subjected to uniform heat flux and rigid inclusion is considered. Using the complex potential functions and conformal mapping function and solving the integral equations, distributions of stress around the inclusions with different shapes are presented. The used method is a complex variable method for an infinite isotropic plate containing a non-circular inclusion. For thesimplicity of the use of the Cauchy integral, the infinite isotropic plate with a rigid inclusion is mapped onto the unit circle. The rotation angle of the inclusion and the bluntness are important parameters that are considered in this study.