First of all, the properties you report don't seem anisotropic at all. I'm assuming you indicate the shear modulus with Exy, Eyx, which I suggest you to rename as Gxy (or Gyx, depending on the convention you choose) to be consistent with the literature. If it's not the case, and Exy is a component of the tensile stress-tensile strain submatrix of the elastic matrix in Voigt notation, you're missing a few values. A full anisotropic material has 21 independent material parameters (due to symmetry of the tensor), you just have 3 (that Exy = Eyx is a result already given by symmetry properties). Thus, my first suggestion is to review your material model.
In general, the Abaqus keyword for elastic behaviour is
*ELASTIC, TYPE = choose type (ANISOTROPIC, ISOTROPIC ...)