This study investigates the effect of composite material stiffness on the accuracy of drilled holes and delamination in the drilling process. Two types of composite materials were tested: glass fiber reinforced plastic (GFRP) and carbon fiber reinforced plastic (CFRP). The drilling process was performed using dedicated drill bits. Samples were clamped in a vice of the Avia-VMC 800 HS vertical machining center. Drilling parameters were maintained constant but unsupported element length was changed. The unsupported element length was defined as an unsupported distance between the drilled hole axis and the sample attachment location. The maximum feed force Ff was determined in the experiments. The accuracy of drilled holes was estimated by optical microscopy. Diameters of the drilled holes were measured. Results made it possible to determine the recommended unsupported element length at which the hole dimensions were within the dimensional tolerance. The study showed a clear decrease in the drilled hole quality and a significant increase in the feed force, especially in the area of tool exit from the workpiece. In addition, the number of delaminated fibers increased with unsupported element length was determined in the study.