The cross-anisotropic elastic material “equivalent” to stratified rock or soil is examined, assuming the individual strata to be isotropic. It is shown that there are restrictions on the ranges of permissible variation of some of the five characteristic constants compared with those of a general cross-anisotropic material. Consideration is given to the special cases in which Charts are presented that allow rapid assessment of the properties of the “equivalent” medium for a range of two-material systems, thus facilitating the application of the elastic solutions for homogeneous, cross-anisotropic bodies to layered media.