The heat transfer problem of a moving source of heat scanning over a semi-infinite solid is of considerable importance for surface processing with high energy beams. The analytical solution of a moving Gaussian beam is extended by superposition of several Gaussian beams in order to approximate real beam shapes, thus providing high flexibility and accuracy. By superimposing two concentric beams, a real intensity profile with a central minimum was approximated with an accuracy of 13&percent; compared to 35&percent; for the conventional Gaussian beam approach. For the corresponding temperature field, an error of 57&percent; for the depth and 17&percent; for the width of the melt pool was eliminated. ©1997 American Institute of Physics.