A method is presented for coupling cubic-order quadrilateral finite elements with the finite side of a new coordinate ascent hierarchical infinite element. At a common side shared by a hierarchical infinite element and an arbitrary number of finite elements, the displacements are minimized in the least square sense with respect to the degrees-of-freedom of the finite elements. This leads to a set of equations that relate the degrees-of-freedom of the finite and hierarchical infinite elements on the shared side. The method is applied to a non-homogeneous cross-anisotropic half-space subjected to a non-uniform circular loading with Young's and shear moduli varying with depth according to the power law. A constant mesh constructed from coupled finite and hierarchical infinite elements is used and convergence is sought simply by increasing the degree of the interpolating polynomial. The displacements and stresses produced by conical and parabolic circular loads applied on the surface are obtained. The efficiency of the proposed method is demonstrated through convergence and comparison studies. New results produced by a frusto-conical circular load applied on the surface of a half-space made up of heavily consolidated London clay are provided. The non-homogeneity parameter and degree of anisotropy are shown to influence the soil response. Copyright © 2012 John Wiley & Sons, Ltd.