The methodology of Peridynamics has been proposed for years and widely used in various engineering fields. The evolution of this theory is always in process, and two major branches appears, namely bond-based and state-based peridynamic method. Recently, a novel concept, peridynamic differential operator, was proposed and adopted in simulation of Newtonian fluid and analysis of structure strength. Just like the intrinsic idea in peridynamic theory, this new operator could convert the partial differential into its integral form so that it would enable the numerical differentiation through integration and avoid difficulties such as discontinuities or singularities encountered in the simulation. Also, unlike the traditional method that the higher order partial differential items are derived from the lower ones, peridynamic differential operator could easily provide differential items with any desired order thus it makes calculation process more efficient and convenient. In this study, the accuracy of peridynamic differential operator is tested by comparing with a given analytical formula. Then, this operator is embedded into the framework of Galerkin method and adopted for elastic deformation analysis in 2D case. The results are compared with those obtained from finite element method and its efficiency and feasibility are verified.