This paper describes a three-dimensional finite element method for modelling two-phase non-Newtonian flows using the power law to describe the non-Newtonian behaviour of the non-wetting and/or the wetting fluid. The fluids can be either dilatant or a pseudoplastic. The technique allows the two-phase flow behaviour to be studied using described empirical parameters for the fluid/fluid interaction. The porous medium may be anisotropic (i.e. it may be described by a variable permeability tensor), and the permeability may be a function of distance in any of the three orthogonal directions. The porosity of the medium may also be defined as a function of the spacial coordinate system. The first application illustrated here is the one-dimensional displacement of a non-wetting fluid by a wetting fluid in a isotropic porous medium. The results illustrate the wetting fluid saturation profile moving through a porous medium, and the effects on the velocity and shape of the profile when changing non-Newtonian and two-phase flow parameters, which gives insights into the choice of drilling fluids. The effects of spatially varying permeability is also investigated and presented here.