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Thermal stresses are important factors in determining the birefringence of optical waveguides. Analytical solutions are developed to estimate the thermal stresses in the core of a buried rectangular channel waveguide. The closed-form solutions for various situations are obtained. The results show that the thermal expansion mismatch between the upper cladding and substrate plays significant role in determining the anisotropy of the thermal stresses in the core. The analytical solutions developed in this paper are consistent with finite element simulations and experimental results.