In this study, ANalysis Of VAriance (ANOVA) and Response Surface Methodology were applied to characterize and optimize laser milling of Carbon Fiber Reinforced Polymer (CFRP) plates. The process was performed by means of a 30W Q-switched Yb:YAG fiber laser, working at the fundamental wavelength of 1064 nm. The machined material was a CFRP plate, 4 mm in thickness, obtained by autoclave cure. According to Design of Experiments (DoE) methodology and previous experiences, a Central Composite Design (CCD) was developed and applied. The investigated parameters were the scan speed, the pulse frequency, the number of repetitions of the geometric pattern and the hatch distance. The suitable milling conditions were obtained from the response surface model. The model allows to set the process parameters to obtain the desired depth with an error <3% and a MRR higher than 1.9 x 10(-3)g/s. POLYM. ENG. SCI., 57:595-605, 2017. (c) 2017 Society of Plastics Engineers