Magnetic stiffness determines the stability of a high-temperature superconductor (HTS) magnetic levitation system.The quantitative properties of the physical and geometrical parameters that affect the stiffness of HTS levitation systems should be identified for improving the stiffness by some effective methods.The magnetic stiffness is directly related to the first-order derivative of the magnetic force with respect to the corresponding displacement,which indicates that the effects of the parameters on the stiffness should be different from the relationships between the forces and the same parameters.In this paper,we study the influences of some physical and geometrical parameters,including the strength of the external magnetic field (B0) produced by a rectangular permanent magnet (PM),critical current density (Jc),the PM-to-HTS area ratio (α),and thickness ratio (β),on the lateral stiffness by using a numerical approach under zero-field cooling (ZFC)and field cooling (FC) conditions.In the first and second passes of the PM,the lateral stiffness at most of lateral positions essentially increases with B0 increasing and decreases with β increasing in ZFC and FC.The largest lateral stiffness at every lateral position is almost produced by the minimum value of Jc,which is obviously different from the lateral force-Jc relation.The α-dependent lateral stiffness changes with some parameters,which include the cooling conditions of the bulk HTS,lateral displacement,and movement history of the PM.These findings can provide some suggestions for improving the lateral stiffness of the HTS levitation system.