The Mindlin theorem and the strain of core in the direction of thickness was considered in this paper. The calculus variation method was then introduced so as to derive the governing equation. The special finite element based on the Mindlin theorem was defined for the face sheet. The nine-node element was used on the displacements u o , v o , w o in the respective directions of x, y, z. The six-node element was also adopted on the rotation angles φ x , φ y in the directions of x and y, which are perpendicular to theyz -plane and the xz-plane. The nodal displacement of the midsurface in the two-face sheet was applied for the sake of indicating the displacement of the core. A smaller degree of freedom was defined so as to avoid the shear locking and obtain a more accurate result.