T E. Fernandez algorithms, based on a solution of the Boltzmann transport equation describing the transport of photons in a specimen, are assembled in a computer program, MSXRF. The algorithms include different treatments of single and double photon collisions undergoing, photoelectric, Rayleigh and/or Compton interactions, polarization effects and Compton broadening. The MSXRF program has been linked to another computer program, TNPP, governing input and output data, calibration parameters, choice of main elements etc. A slightly different approach to a calibration procedure is proposed, which makes use of the hybrid MSXRF-TNPF program. This lining-up procedure is based on measurement of a pure calibration standard and is a 'one-point' determination of the analytical curve. The model is examined and adjusted by using a set of international standards covering a range from ppm levels to the highest concentrations. The same international standards are also used to control and describe the performance characteristics of the analytical method. The new calibration procedure is simpler in comparison with the earlier used. Analytical results, evaluated by the MSXRF-TNPP program of measured CRM standards, have been compared with results from an earlier investigation, evaluated by the TNPP program only. The latter program is cruder in its design with regards to existing theories and setting of parameters and is not applicable over large concentration ranges without using correction factors for scattering and other specific effects. The results achieved were comparable to those from the production TNPP program. Problems such as the processing time, which is of utmost importance when applying a program in practice, is discussed. Today the evaluation time is unacceptable but an execution time of only a few minutes is reckoned to be good with new strategies. Copyright (C) 2001 John Wiley & Sons, Ltd.