The smoothing of finite element meshes with triangular elements is basically equivalent to the optimization of the finite element mesh. To formulate the optimization problem different quality measures can be used. One of the aims of the paper is to investigate the use of the different quality measures. To study the quality measures initially an internal mesh point is considered with all attached triangles. Combining the quality measure of the triangles around the internal mesh point a mathematical surface is derived. There are several ways to derive the surface with different mathematical "combinations", for example: sum, quadratic-sum or multiplication. According to the characteristics of the surface the interior mesh node can be replaced into the maximum or minimum of the surface. This extremum will provide the optimum position of the internal mesh node. Another goal of the paper is to determine whether the results are dependent on the used quality measures or not.