Magnetic hysteresis rods have been used successfully for damping the attitude motions of passively stabilized near-Earth satellites. This paper describes the implementation of a model of magnetic hysteresis that is suitable for digital computer simulations of such motions. The model is based on the domain theory of magnetization which assumes that associated with each domain is a shifted rectangular hysteresis loop. Coefficients used by the model are determined by least-squares fitting data from experimental hysteresis loops. For a type of hysteresis rod commonly in use, it is shown that a simplified version of the model may be used. Results from the theoretical model are compared with experimentally generated loops and show good agreement. Nomenclature a, b = axes of increasing and decreasing H in the theoretical hysteresis model B = magnetic flux density in a damping rod Bn = B(Hn)j the normal flux density in a rod Br = B(Hr) — B(Q), the residual flux density in a rod dA = weighted differential area in the Preisach plane F = function minimized in determining kQ and the fct-/s H = ambient magnetic field component along the longitudinal axis of a damping rod Hn = normal magnetizing force along the axis of a rod Hr = 0, the residual magnetizing force along the axis of a rod kotkij = coefficients determined by least-squares fitting experimental data to the theoretical model N = parameter that determines the order of the polynomials Pij Pij = polynomials in terms of H and Hn used in the theoretical model aij,pij = coefficients of Hn when only the normal and residual experimental magnetization data are used