Under unfavorable conditions, errors even five to ten times larger may occur for certain wellbore directions. Thus, the drilling fluid may degrade the, borehole position accuracy sufficiently to reduce the possibility of hitting the planned target. The commonly used model for estimating wellbore position accuracies [2,3] does not include this effect. For some directions the presence of the phenomenon can be discovered by using the appropriate acceptance criteria [4]. Nevertheless, there is a need for a general approach to quantify and reduce this troublesome influence on the magnetic sensor readings. The magnetic properties of a drilling fluid can vary significantly, depending on several factors, including the mineralogical composition of the drilling fluid additives [5], the bulk transferring procedures, and the circulation properties of the drilling fluid [6]. In the present paper we analyze how magnetic sensor readings are influenced by the magnetic susceptibility of the drilling fluid. We restrict ourselves to a sufficiently long straight section of the borehole. The problem then reduces to finding the field induced by the Earth's magnetic field inside an infinite cylinder, containing a weakly magnetic material (the drilling fluid), with an embedded inner region containing the magnetometers.