Further application of an efficient novel meshfree technique based on the moving kriging (MK) interpolation for static and dynamic analyses of two-dimensional piezoelectric structures is presented. The MK scheme is used for constructing the shape functions which satisfy the Kronecker delta property. Hence, the burdensome task of enforcing the essential boundary conditions as in the moving least-squares approximation is avoided. The mechanical displacements, electric potential and natural frequencies of structures are investigated in detail through a series of numerical examples that are to demonstrate the applicability and the efficiency of the proposed method. The results obtained are then compared with those of other available reference solutions with very good agreement.