The main aim of this paper is to present the method to evaluate the stress distribution around quasi-rectangular hole in infinite isotropic plate subjected to uniform heat flow at infinity. The used method is the development of the Goodier and Florence’s method for the thermoelastic problem of uniform heat flow. Goodier and Florence used their solution for stress analysis of isotropic plates with circular and elliptical holes. In order to expand this method to solve the perforated plates with non circular holes, by means of conformal mapping, the infinite area external to the hole can be represented by the area outside the unit circle. In this paper, thermal-insulated condition along the hole boundary is assumed. Amongst the important parameters in hole geometry are rotation angle of hole, bluntness and aspect ratio of hole size. The results obtained demonstrate the effect of these parameters on stress distribution around quasi-rectangular hole and the correct selection of these parameters, lowest thermal stress rather than amount of stress corresponding to circular hole can be achieved. This method can be used for study of the stress analysis of plate with various holes.