A quasi-static axisymmetric solution is obtained of the fully coupled diffusion-deformation system of equations for a poroelastic half-space possessing anisotropic permeability and compressible solid and fluid constituents. This solution is used to study analytically the deformation of a half-space by surface loads. The problem of normal disc loading is discussed in detail. The effects of the compressibility of the solid and fluid constituents and the anisotropy in permeability are studied numerically