The main objective of the paper is to outline the 'bridges' existing between the outcomes of fundamental researches and the results of investigations in the field of industrial laser materials processing (LMP). An analysis is presented on the models based on non-stationary hydrodynamic phenomena caused by deeply penetrating high power CW laser beam into materials. This is typical of laser welding (LW) and laser cutting (LC). A physical analysis pertaining to melt removal and melt layer instability mechanisms of gas jet assisted CW-CO 2 laser fusion cutting is presented. The models deliberated here are melt squeezing out by gas pressure gradient, melt dragging by the friction force between melt surface and gas flow, formation of moving shelves at the cutting front. In case of high laser intensity, radiative flux interacts with material causing dynamical thermal transport onto the surface and phase transition at solidliquid-gas interfaces. The solution is based on the non-stationary variables. Under these conditions the Mach number varies significantly due to laser intensity associated with laser flux energy instabilities. The connection among material surface temperature, laser intensity, laser flux and pressure in the plasma cloud is brought out. In addition, novel mechanisms based on hydrodynamics are proposed.