Abstract The electromagnetic force acting on a high- T c superconductor (HTSC) is evaluated in an axisymmetric problem by using the boundary element method (BEM). Application of the BEM is useful since the open boundary is treated in the problem. Nonlinear constitutive relations between screening current and electric field are important in the numerical analysis. When a permanent magnet is moved towards and away from the HTSC, the levitation force between the magnet and the HTSC shows hysteresis properties, and repulsive force often changes to attractive force. The BE solutions are in good agreement with experimental results. Gradients of major and minor loops of the force are also evaluated with respect to spring constants.