The characteristics of electroacoustic surface waves supported by a curved piezoelectric‐vacuum boundary are studied. A coaxial structure with a piezoelectric insulator as the inner cylinder and an electric conductor as the outer cylinder is considered. A dispersion relation for electroacoustic surface waves circulating around the periphery of the piezoelectric cylinder is obtained. Asymptotic solutions are compared with numerical solutions. Profiles for the mechanical displacement and electric potential for various modes are presented. Possible application as delay lines with long‐time delay is indicated.