During laser materials processing the direct interaction between the laser beam and the processing zone essentially determines the process. A self-regulating processing front develops. A simplified mathematical model was applied to describe this first order mechanism. In particular, a high power Yb:fibre laser beam was characterized and modelled. The dependence of the keyhole shape on different beam models was studied. While a top-hat beam would cause a very different interaction, the impact from the more accurate beam model hardly differed from a Gaussian beam, as can be explained by interaction solely with selected peripheral domains of the beam.