Abstract: A theory of elasticity for the bending of orthogonal anisotropic beams has been developed by analogy with the special case,which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two deminsions.In this paper,we present a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger.It is pointed out that Reissner's theory to account for the effect of transverse shear deformation is not very approximate in the components of stress.