The aim of this paper is to study the thermal stress analysis in a plate with a hole in a hyperelliptical shape assuming the state of plane stress. The system of stress is analyzed using complex variable method under isothermal conditions. The high stress concentration found at the edge of a hole is of great importance, therefore stress system at the tip and in the neighborhood of the tip of the hole are also studied. Numerical calculations are computed for material steel and contour graphs are depicted to show the obtained results. Key words: Azimuthal stresses, complex variable method, thermal stresses, plane stress.