This paper discusses the development of a procedure for computing creep and stress relaxation at the critical location in a through-hole structure. A high-speed methodology was developed for calculating cyclic creep and stress relaxation at critical locations of a pile on elastic foundation subjected to cyclic thermomechanical loading. This simplified analysis was exercised for two cases involving a pile on elastic foundation problem with different thermomechanical loading. The simplified analysis exhibited no computational problems and gave a stable solution for the full dwell times. Comparisons made with experimental results for these cases gave an excellent agreement at a much faster computing time. This simplified procedure is expected to be even much faster when an entire pile on elastic foundation assembly is analyzed.