The mathematical modeling of the laser cutting of steel plates is considered here by implementing the model proposed by Niziev and Nesterov, as formulated in . The 3D-cutting front is described, according to this model, by a highly nonlinear partial differential equation. A number of simplifying assumptions can be formulated, however, so that this complex equation can be handled more easily. This enables us to concentrate on the physics of the model, rather than having to struggle with its mathematical manipulations. This simple model confirms in a capturing way the conjecture originally launched in  that cutting speed can be increased with a factor of about 1.5 to 2 by switching over from circular to radial polarization. As a further consequence, the model predicts that a similar improvement is also found regarding the plate thickness at a constant cutting speed.