The paper deals with a mathematical magnetic field model for evaluating the magnetic iron losses in steel laminations which are used in electric machinery. The magnetic hysteresis and the eddy current effects are directly and simultaneously taken into account. Hereby, the commonly used analytic expressions for the distribution function in the widely adapted preisach hysteresis model are found to be not quite accurate. The magnetic circuit is decomposed into magnetic and air gap network elements, the former showing a finite element structure. Although the model retains the essential features of a cumbersome 3D problem, a relatively simple algorithm may be developed.