A theoretical analysis of steady-state heat conduction through homogenous fouling on the external surface of tubes in cross-flow has been made. Modelling the fouling geometry as an eccentric annulus, a finite difference procedure in bipolar coordinates has been developed to predict the effect of fouling on the thermal performance. Theoretical predictions for a range of geometry, thermal conductivity and variable convection boundary conditions are presented. It is shown how, for a range of foulant thickness, eccentricity and thermal conductivity, the rate of heat transfer to a given size tube can be reduced or increased. The case of non-homogeneity of the fouling is explored with a view to extending the analysis towards varying thermal conductivity.