AbstractThis paper presents a parallel Galerkin boundary element method for the solution of surface radiation exchange problems and its coupling with the finite element method for mixed mode heat transfer computations in general 3‐D geometries. The computational algorithm for surface radiation calculations is enhanced with the implementation of ideas used for 3‐D computer graphics applications and with data structure management involving creating and updating various element lists optimized for numerical performance. The algorithm for detecting the internal third party blockages of thermal rays is presented, which involves a four‐step procedure, i.e. the primary clip, secondary clip and adaptive integration with checking. Case studies of surface radiation and mixed heat transfer in both simple and complex 3‐D geometric configurations are presented. It is found that a majority of computational time is spent on the detection of foreign element blockages and parallel computing is ideally suited for surface radiation calculations. Results show that the decrease of the CPU time approaches asymptotically to an inverse rule for parallel computing of surface radiation exchanges. For large‐scale computations involving complex 3‐D geometries, an iterative procedure is a preferred approach for the coupling of the Galerkin boundary and finite elements for mixed mode heat transfer calculations. Copyright © 2004 John Wiley & Sons, Ltd.