In this paper,with the aim of understanding the behaviors of the green materials such as wood and poly-L-lactic acid,both of which are piezoelectric bodies with D∞ symmetry,we theoretically analyze the electroelastic field in such a body subjected to an electrical loading.As an analytical model,we treat a solid and infinitely long cylinder subjected to a transverse electric field due to a non-axisymmetrically distributed electric surface potential.We introduce the displacement and electric potential functions to express the displacement and electric field in the body and obtain theft governing equations using the fimdamental equations for the electroelastic field.As a result,the electric potential and the components of the displacement,strain,stress,electric field,and electric displacement are expressed in terms of four functions:two elastic displacement potential fimctions and two piezoelastic displacement potential functions,each of which satisfies a Laplace equation with respect to the spatial coordinates transformed appropriately by the material properties.Then,the goveming equations for the potential functions are solved by the Fourier transforms with respect to the axial coordinate and the Fourier series expansions with respect to the circumferential coordinate.As a result,the analytical solutions of the electroelastic field quantities are obtained.Performing numerical calculations,we elucidate the electroelastic field quantities within the cylinder and find unique electroelastic coupling behaviors,which clearly demonstrate the necessity for the theoretical analysis presented.