This paper presents a preliminary study of mathematical modeling and numerical simulation of laser engraving process. The 1-D simulation concerned CO2 c. w. pulsed laser engraving of plasma sprayed Cr2O3 coatings as used in the manufacture of anilox rolls. The thickness of the evaporated material was calculated as a function of laser processing parameters viz. pulse length and power density. The actual thermophysical coefficients of plasma sprayed chromia were used if available and the results of calculated thickness of evaporated layer are compared with the experimentally determined depth of engraved cells to estimate unknown coefficients of liquid chromia. Finally, the experimental effect of overflow was related to the calculated thickness of liquid layer. The experimental procedure of minimization of this effect is proposed.