A technique for numerical integration of the finite difference (matrix) formulation of the unsteady heat transfer equation has been applied to the thermal stress analysis requirements of ASME B&PV Section III, Article NB-3650. This technique, with its properties of unconditional solution stability, has been incorporated into a new computer program, TRANS2A, which has been designed totally around the needs of the stress analyst. To be of maximum aid to the analyst, in addition to the necessary output of thermal gradients (ΔT2 and ΔT2 ) and average temperatures (Ta and Tb ), TRANS2A provides a complete set of thermal stress histories and tables of thermal stress extrema. Values of the thermal stresses are output at maxima of the thermal gradient terms (with or without adjacent sections), in addition to the extrema of the secondary and secondary plus peak stresses and time of occurrence. Each solution is performed for a set of seven general and three optional stress indices. The process allows a strict and simple data interface to the combined stress analaysis computation without excessive approximations. Data may also be stored so that sections need not require repeated analyses. All computational output, from the detailed heat transfer solution to the stress summaries, may be requested or deleted at the option of the analyst. For generality, TRANS2A includes a complete set of temperature-dependent material properties for all current piping materials and a complete set of fluid properties for water, steam, and sodium. Fluid transient data are input using phase and temperature, and a choice of four flow rate specifications. Accepted heat transfer correlations for laminar and turbulent flow in liquids and gases are included, with smoothing at two-phase excursions. Samples of the TRANS2A benchmark problems are included, with discussions on data interface and sensitivity for erratic fluid transients.