The equilibrium of a thin compressible elastic membrane has been considered. In the present work the theory developed in that paper (3) is applied to the periodontal membrane which lies between the tooth and the jaw-bone.For simplicity, a tooth is considered of which the root is a right circular cone, the thickness of the membrane being assumed constant. A load is applied to the tooth in a plane containing the axis of the root and a determination is made of the resulting stress in the membrane and displacement of the tooth.It is also found that the periodontal membrane holds the tooth in place in a way different from that commonly accepted by dentists.