In this study, the mechanical design and analysis of a magnetic levitating linear bearing suitable for working in the non-hysteretic range of forces is presented. The semi-cylindrical design of the superconductor provides stable equilibrium positioning and restoring forces in all degrees of freedom except for two with a cylindrical magnet floating along the axis of revolution/displacement. Using finite element analysis, it has been proven that the magnet can float stably and passively in a complete non-hysteretic Meissner state. This non-hysteretic passive linear bearing could be suitable for long-stroke precision positioning. The high translational symmetry of the magnetic field seen by the superconductor assures a usable long stroke of around ±90 mm with full performance and ±150 mm with reduced performance. This linear bearing in combination with an actuating system for only one degree of freedom could be used for accurate precision positioning systems for cryogenic environments with zero hysteresis in the movement.