Abstract: A varying thickness plate element belonging to three-variables hybrid displacement model is derived and tested. The matrices of this element are expressed in explicit form. Derivation and application of hybrid displacement model are also discussed briefly. It is pointed out that the functional of hybrid displacement model with three-variables is more directly than that with two-variables when they are used in derivation of varying thickness plate element. It is also cleared up that there are two possibilities to obtain concrete expressions of element matrices when three-variables functional is adopted.Numerical calculations for some specific examples are obtained and compared with existed exact solutions. The results obtained are better than those from Slyper's Nonconforming model which is commonly used in engineering, and superior to those from the simplified hybrid displacement model developed by the authors of this paper formerly.