In this study we model formation of ice bands in the marginal ice zones. A one-dimensional coupled ice-ocean model is used in which the ice model is coupled to a reduced gravity ocean model through interfacial stresses. The internal ice stresses are important only at high ice concentrations (90%--100%); otherwise, the main balance for the ice motion is between the air-ice stress and the ice-water stress, i.e., free drift. The drag coefficients were chosen so that the air-ice momentum flux is 3 times greater than the air-ocean momentum flux. Thus the Ekman transport is larger under the ice than in the open water, so that winds parallel to the ice edge, with the ice on the right, produce upwelling. The upwelling simulation was extended to include temporally varying forcing, which was chosen to vary sinusoidally with a 4-day period. This forcing resembles successive cyclone passings perpendicular to the ice edge. When the oceanic upper layer was thin, which means that the dynamics are strongly nonlinear, the ice bands were formed. The up/downwelling signals do not disappear in wind reversals because of nonlinear advection. This leads to convergences and divergences in oceanic and ice velocities that manifest themselves as ice banding. At least one wind reversal is needed to produce one ice band.