Drilling fluid filtrate invades the pores of rock surrounding a well bore during drilling of the well, and contaminates the pore fluid originally within the rock pores. Models for the flow of contaminated pore fluid towards a sampling tool within the well bore are investigated, assuming that the filtrate has the same viscosity as the original pore fluid and that the wellbore radius is small compared to the depth of filtrate invasion. If the filtrate contamination in the fluid withdrawn from the rock is monitored as a function of the volume withdrawn, then it is shown that results can be inverted to give the radial distribution of filtrate around the well bore. A new generation of guarded sampling probes is then considered, and it is shown that the radial distribution of filtrate can be obtained by means of such a probe if the fraction of flow entering the central sampling region of the probe is small compared to that entering the concentric annular guard probe. The effects of dispersion, non-zero wellbore radius and anisotropic hydraulic permeability of the rock are also studied, and numerical simulations are used to give some indication of the effect of the ratio of the filtrate viscosity to that of the original pore fluid.