For axisymmetric piezoelectric cylinder, the reciprocal theorem and the axisymmetric general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the cylinder of general edge geometry and loadings. A decay analysis technique developed by Gregory and Wan is converted into necessary conditions on the end-data of axisymmetric piezoelectric circular cylinder, and the rapidly decaying solution is established. The prescribed end-data of the circle cylinder must satisfy these conditions in order that they could generate a decaying state within the cylinder. When stress and mixed conditions are imposed on the end of cylinder, these decaying state conditions for the case of axisymmetric deformation of piezoelectric cylinder are derived explicitly. They are then used for the correct formulation of boundary conditions for the theory solution (or the interior solution) of axisymmetric piezoelectric cylinder. The results of the present paper enable us to establish a set of correct boundary conditions, most of which are obtained for the first time.