In the aeronautical industry, carbon fibre reinforced polymers (CFRP) are increasingly used. CFRP composites enable the production of complex shapes, which leads to reduced number of required components, lower total weight and enables higher stength of the products comparing to the conventional materials. Great strength and the heterogeneity of the material present problems in contact machining. Problems also occur in non-contact laser processing. The epoxy resin serves as a binder for carbon fibers and is partially transparent in both the visible and the infrared spectrum, causing causing low absorption of laser light. We examined the basic mechanisms of laser ablation and tested the thesis about the dyeing of epoxy resins for the purpose of increasing the absorption of laser light. With the help of existing literature and by a systemativ experimental approach to the experiment, we examined the thesis. We used most of the commercially available dyes of various industries, as well as a few purpose-developed pigments exclusively dedicated to laser marking. We found that the dye slightly improve the cutting characteristics of the epoxy resin itself. Rather dyeing is significantly more important cutting patern. The most effective is engraving cuts, which consists of short cutting crossings at an angle of +- 45◦. We have found the importance of the parameter ''skip line'', which dictates the sequence of transitions of the sample engraving. The results confirm the thesis of increasing the absortiveness of the colored epoxy resin. The most important finding is the systematic management of the laser beam for improved cutting properties of CFRP materials.