Fissures of varying sizes, orientations and surface coatings present in Scottish lodgement tills influence their mass permeability and consolidation rates, inducing three-dimensional anisotropy in these properties. Satisfactory laboratory measurements require the costly testing of large specimens. This paper calculates the contribution of a discontinuous fissure to the flow through a fissured region by use of the finite element method and presents a method of prediction of mass permeability and its three-dimensional anisotropy by empirical computer-aided models based on the observed properties of the fissures and of the intact blocks. The results of such predictions have been found to compare satisfactorily with those from actual tests on relatively large undisturbed till samples of various orientations from three sites in West Central Scotland. Such a method is expected to reduce sampling and testing requirements for the above properties of fissured tills and possibly other similar soils.