This paper describes a numerical procedure for modelling mud cake growth and fluid invasion during drilling. Two three-dimensional finite element programs have been developed, one to model the non-Newtonian flow of the drilling mud in the annulus between the drill string and the borehole wall, and the other to model the non-Newtonian multiphase flow of the fluid base of the mud into the surrounding porous formation. These are integrated into a time-stepping routine and a crossflow microfiltration model is employed to predict the increase in cake thickness at nodes on the borehole wall at each time step. The procedure is applied to the model of a borehole with an eccentric drill string giving the thickness of the cake, the velocity of the permeating fluid and the saturation of the fluid in the surrounding formation at different times. The effects of changing the eccentricity of the drill string and the power law exponent of the mud are also investigated.