This article focuses on investigating the steady state heat conduction through the walls of heat exchanger tubes of any arbitrary geometry using a numerical technique called boundary element method (BEM) for two different cases. In the first case, the problem is studied for exchanger tubes where both the inner and outer surfaces are maintained at isothermal condition. Secondly, BEM is used for the prediction of heat transfer through exchanger tubes with the inner surface kept at a constant temperature and the outer surface subjected to convective condition. A two dimensional semi-analytic technique called boundary collocation method (BCM) is also used to solve the same two dimensional heat conduction problem for the purpose of comparison. The conduction shape factor (CSF) calculated through BEM for all the shapes in the first case shows excellent agreement with that obtained through BCM and other published results. Further, the heat transfer calculated by BEM is in good agreement with that obtained through the numerical software Ansys Fluent (R). For both the cases, the temperature profiles computed by BEM match very closely with those generated through Ansys Fluent (R). The problem has been solved for some exchanger tubes having different types of geometries which pose numerical complication in grid-based techniques. The excellent agreement of the results of BEM with the existing results shows the accuracy and efficiency of the method. (C) 2016 Elsevier Ltd. All rights reserved.