Paper presents a study of modeling and numerical simulation of laser engraving process. The 1-D simulation concerned CO2 c.w. pulsed laser engraving of plasma sprayed alumina, titania and aluminum titanate coatings. These coatings will possibly replace the Cr2O3 ones used currently in manufacturing of anilox rolls. The model was refined in comparison to the previous one (1) by taking into account the speed of the roll at the engraving. The actual thermophysical coefficients of plasma sprayed alumina, titania and aluminum titanate were input to the computations. The model enabled calculation of the engraving's depth in function of the principal laser treatment parameters viz. pulse length and laser power density. Finally, the overflow effect at the laser treatment of new ceramics was discussed and compared to that occurring at Cr2O3 engraving.