The objective of present research works is to investigate the effects of process parameters, including the power of laser, cutting speed, material thickness, and the edge angle, on the melted area in the sharp edge of the cut material fur the case of cutting of a low carbon steel sheet using high-power CW Nd:YAG laser. In order to investigate the influence of edge angle and size of loop on the melted area in the sharp edge, angular cutting tests and loop cutting tests have been carried out. From the results of angular cutting tests, the relationship between the edge angle and the melted area has been obtained. The results of the experiments have been shown that the melted area is rapidly reduced from $120^{circ}$ of the edge angle and the melted area is nearly zero at $150^{circ}$ of the edge angle. Through the results of loop cutting experiments, the relationship between the cutting angle on the melted area in the edge according to the size of loop have been obtained. In addition, it has been shown that a proper size of loop is nearly 3 mm as the corner angle is greater than $90^{circ}$ and 5 mm as the comer angle is less than $90^{circ}$. The results of above experiments will be reflected on the knowledge base to generate optimal cutting path of the laser.