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An analytical method is presented for the calculation of 1 thermal stress and the material birefringence in polarization-maintaining 1 optical fiber. The method is based on the thermoelastic displacement c potential in which the principle of superposition applies. The method is applicable to any fiber structure. Its application to fibers with isolated stress-producing regions and a variety of core shapes is demonstrated. The optimum fiber parameters required to achieve maximum material birefringence for fibers with circular or bow-tie shaped stress regions are given. It is also shown that the thermal stresses tend to make the bow-tie fiber more crack-resistant than the fiber with circular stress lobes.