The article introduces a method to create any 2D laser profiles applied in welding technology. This method allows for the creation of profiles that best suit the weld characteristics and material of the weld workpiece, thereby improving the quality, accuracy, and aesthetics of the weld and increasing laser welding efficiency. In the study, the authors proposed a model of a 2D laser profile generation system with a reflecting mirror and two piezoelectric linear actuators. The forward and inverse kinematic equations were completely solved, while a control algorithm was proposed to control the motion of linear actuators. The model is simulated on MATLAB with circular, sin-wave, and 8-figured profiles. The obtained results show that the control profiles are almost close to the desired ones (both shape and scan period). There is a displacement between them. With the given simulation parameters, the displacements of the above-mentioned profiles are 0.03 mm (1.5%), 0.05 mm (2.5%), and 0.05 mm (1.25%), respectively. This shifting can be reduced by increasing the number of samplings. The simulation results provide strong evidence for the feasibility of implementing a practical 2D laser profile generation system based on the proposed model.