The known absolute nodal coordinate formulation (ANCF) uses magnitudes of position vector and their gradients as finite element nodal coordinates. In this paper, the efficiency and domain of application of classical finite element method (FEM) and ANCF have been studied by considering some numerical examples. The authors use known rectangular 48 DOF ANCF and 36 DOF ANCF elements and classical FEM elements of thin shells analysis. A comparison of convergence and computation time of these methods is made, together with a discussion of their advantages and disadvantages. The ANCF follows from the known mixed FEM. This connection is not discussed.