The interaction between two polymer brushes (layers of polymer chains grafted at one end onto an impermeable surface) brought into a close contact and moving with respect to each other in the lateral direction is studied by the method of stochastic dynamics simulation. The structural properties of the brushes such as the monomer density profile, the distribution of the free ends of the chains, as well as the disjoining pressure have been studied as functions of the separation between grafting planes (the degree of static overlapping of brushes) and of the lateral displacement rate. We have found that at zero shear rate the extension of grafted chains perpendicular to the grafting planes monotonically decreases with decreasing distance between the planes, but not as rapidly so that significant overlapping and interpenetration of brushes occurs. At strong compression the free ends of the chains are distributed all over the gap between grafting planes. An increase in the shear rate is accompanied by inclination and extension of chains in the direction of shear and by a simultaneous decrease in the chain dimensions in the direction perpendicular to the grafting planes : the free ends an localized near the middle plane and progressive decoupling of brushes occurs. At large shear rate the width of the interpenetration zone almost vanishes. The inclination of chains at given shear rate increases with decreasing grafting density and decreasing width of the gap between the grafting planes. The disjoining pressure exhibits a weak maximum as a function of the shear rate that is in qualitative agreement with the predictions of scaling theories.