We derive the long wave length equivalents of the constitutive relations for finely stratified fluids as suggested by Saito and Abe [1984>. The results show the transversely isotropic relations characterized by two effective viscosities. One is associated with shear stress applied on the plane parallel to the layering and the other is with normal stress applied perpendicular to the layering. If thin soft layers exist in the low velocity zone, there may be a significant difference in these two viscosities. A simple calculation simulating mantle flow with large apparent anisotropy shows the possible existence of convection having large aspect ratio.