A reliable design via FEA techniques is highly dependent on the execution of an analysis which is accurate and represents the design precisely. The accuracy and efficiency of the two available methods of meshing of the design components (mapped and free meshing) for finite element analysis are addressed in this paper. This paper intends to clarify that the “shape” of the elements rather than the “pattern” is the distinguishing factor for accuracy of the mesh-quality-results. This paper concludes by comparison of the FEA analysis to the analytical theory that element integrity and results are not governed by the elemental aspect ratio alone. The mesh density has a greater effect. Four types of mesh are investigated and compared for results' accuracy. In specific, a low-density free mesh, a high-density free mesh, a mapped mesh with high aspect ratio, and a mapped mesh with low aspect ratio of a plate with center hole are examined and compared. A plate with center hole is selected for this purpose since its far-field structural behavior is predictable and is highly applicable in showing the differences in accuracy among the different meshing methods.