A one-dimensional model is presented to study the main characteristics of magnetized fluidized beds. The Foscolo and Gibilaro particle bed model is assumed as the basis for the evaluation of the fluid-dynamic contributions to stabilization, while the magnetic forces are expressed according to Rosensweig and Ciprios (Powder Technol. 64, 115-123, 1991). The stability limit is derived and the Kotchine analysis is applied to the model to study the structure of the discontinuities arising from the system of hyperbolic PDEs. This allows a qualitative understanding of the effects due to magnetic forces acting on the particles. The present study is mainly focused on the effect of a magnetic field which is not sufficient to stabilize the bed, i.e. magnetized bubbling fluidized beds. Qualitative effects on both the particle phase and the gas phase are discussed.