Since the demagnetisation curves of permanent magnets with knee points are not single-valued, hysteresis effects below the knee points need to be considered. A field problem with an unknown and nonuniform permanent-magnet source distribution occurs. A hysteresis model for simulating permanent magnets with such knee points is presented in the paper. By using the model and a permanent-magnet source-iteration method, the field problem can be easily solved by the finite-element method. The field solutions for both a single magnet and a magnet assembly, each air-stabilised, are computed by the presented method, and are found to be in good agreement with test results.