Abstract Methods for analysing conductive heat flow with applications to underground earth contact systems are reviewed. A discussion and comparison of both the finite difference and finite element methods are presented. The effect of domain discretisation on accuracy for both methods is presented. One- and two-dimensional models are derived and used to solve selected problems. The results for various discretisation domains are compared and constrasted. The application of both the finite difference and finite element approaches to the analysis of heat transfers in an underground building is given. Recommendations are made to aid in the selection of the numerical techniques that are the most appropriate for analysing conductive heat flow problems. Finally, a statement is made on the analysis of the three-dimensional heat and moisture transport problem associated with underground earth contact systems.