This paper proposes a new cylindrical geometry design for the zero field cooled (ZFC) Maglev system. In previous research, a ZFC-Maglev of rectangular geometry was designed and an experimental prototype, with a magnetic track, was developed. Studies on this system showed that the Maglev is prone to derailing, mainly due to the nonlinear nature of the guidance forces. A cylindrical geometry is proposed which allows to solve those situations, making the ZFC-Maglev inherently stable and with a linear lateral restitution force. A 3D model was made, using COMSOL Multiphysics®, where several cylindrical geometries were developed, to study the viability of these solutions regarding the levitation and guidance forces. It is shown that the cylindrical geometry is a viable solution, being naturally stable and having a linear response to lateral forces. However, the cylindrical geometry presents two major drawbacks, which are the limitation of lateral movement and the possibility of flux pinning occurring between the HTS and the permanent magnets.