This study is aimed at the modelling of mesoscale processes such as up/downwelling and ice edge eddies in the marginal ice zones. A 2-dimensional coupled ice-ocean model is used for the study. The ice model is coupled to the reduced gravity ocean model (f-plane) through interfacial stresses. The constitutive equations of the sea ice are formulated on the basis of the Reiner-Rivlin theory. The internal ice stresses are important only at high ice concentrations (90-100%), otherwise the ice motion is essentially free drift, where the air-ice stress is balanced by the ice-water stress. The model was tested by studying the upwelling dynamics. Winds parallel to the ice edge with the ice on the right produce upwelling because the air-ice momentum flux is much greater than air-ocean momentum flux, and thus the Ekman transport is bigger under the ice than in the open water. The upwelling simulation was extended to include temporally varying forcing, which was chosen to vary sinusoidally with 4 day period. This forcing resembles successive cyclone passings. In the model with thin oceanic upper layer, 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 which manifest themselves as ice banding. At least one wind reversal is needed to produce one ice band.