The paper is about a medium size and cost effective carbon dioxide (CO2) gas discharge computer numeric control (henceforth, CNC) laser cutting and engraving machine. The main attention is given to the improvement of processing quality with plane based laser beam positioning using a linear mirror delivery system. The summary of these dependencies have been gathered and observed from a self-built CNC laser machine prototype. The laser beam is a fraction of a millimeter in diameter and the errors of the machine are transferred to the cut of the material. To improve cut quality, the frame of the construction as well as the positioning element dynamics should be analyzed. The frame of the machine must withstand the forces from the movement of the laser head; therefore it is necessary to determine the impact of these forces on the frame. A finite element method analysis was made with Solidworks. Insight in ways to increase the structural stability was made and with minimum costs an optimal solution was found. It was shown that the quality of the positioning depends on the belt drive and the stepper motor. Whereas the stiffness of the belt and the full revolution step count of stepper motor (or step resolution) and torque play a substantial role. The gathered information of the quality affecting factors is suitable for engineers that are involved in the building process of CNC laser cutter device or as a guide to troubleshoot errors on a working machine.