The behavior of supercooled polymer melt composed of short chains with ten beads between rapidly oscillating plates is simulated by using a hybrid simulation of molecular dynamics and computational fluid dynamics. The flow profiles of polymer melt near an oscillating plate are quite different from those of Newtonian fluid. The viscous boundary layer of the melt is much thinner than that of the Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid when ftR < 1, and the crossover between the liquid-like and solid-like regime takes place around ftR = 1 (where f is the angular frequency of the plate and tR and ta are the Rouse and the alpha relaxation time, respectively).