On the basis of the two-dimensional elasticity theory,the stress distributions of simply supported orthotropic beams with arbitrarily and continuously varying thickness are investigated.The general expression of stress function,which exactly satisfies the governing differential equations and the boundary conditions,is derived.The unknown coefficients in the stress solution are approximately determined by using the Fourier sinusoidal series expansion on the upper and lower surfaces of the beam.The present solutions ensure a rapid convergence and are in a good agreement with those obtained from a commercial finite element software ANSYS.The proposed method overcomes the limitation of the conventional beam theories that fails to consider all elastic constants for orthotropic materials.With the aforementioned features,the method could be applicable in aerospace engineering and other projects with highly accurate demand on stress analysis such as the design of micro-mechanical apparatuses.