Abstract: In this paper, it is pointed out that under both plane stress and plane strain deformation conditions, the constitutive and equilibrium equations in the plane of isotropy of a transversely isotropic body can be expressed in a form identical to that for an isotropic body. This equivalence is implemented through the introduction of a mixed constant containing the Poisson ratios of the transversely isotropic medium. The introduction of this constant eliminates an inconsistency that appeared in the literature on the solution of transversely isotropic bodies. The use of this constant also facilitates consideration of transverse isotropy of the constituents of unidirectional fibre reinforced composite materials.