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With the aim of understanding the behaviors of the green materials such as wood and poly-L-lactie acid,both of which are piezoelectric bodies with D∞ symmetry,we theoretically analyze the electroelastic field in 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 their governing equations using the fundamental equations for the electroelastic field.The governing equations for the potential functions are solved by the Fourier transform and expansion techniques.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 eleetroelastic coupling behaviors.