Flax reinforced epoxy (F-Ep) composites were prepared by the compression moulding technique, varying the fiber content (0, 25, 35 and 45 wt%). The free vibration test was performed on the neat epoxy and F-Ep composites to understand their dynamic characteristics, and results showed that natural frequency and damping factor of the F-Ep composites increased with an increase in the fiber content. The F-Ep composite (45F-Ep) that exhibited better damping was selected for performing the drilling operation. Factors such as spindle speed (rpm), feed rate (mm/min) and drill point angle (degree) were chosen as input parameters and the tabulated set of experiments were in accordance with Taguchi’s design of experiment. The response measured was thrust force and the obtained values were found in the range of 19.66 to 50.75 N. The minimum value of thrust force was achieved when the F-Ep composite was drilled at high spindle speed (3000 rpm), with a feed rate of 75 mm/min using the drill point angle of 118°. ANOVA analysis showed that the developed regression model was significant and thrust force was mainly influenced by the spindle speed. Mathematical models were developed for drilling F-Ep composite using response surface methodology (RSM) and adaptive neuro fuzzy inference system (ANFIS) and compared for their efficacy.