We investigate, by extensive molecular dynamics simulations as well as a simplified single-chain model, the influence of steric hindrance on the dynamic properties of nonentangled chains in polymer melt due to confining surfaces. We extend the Rouse model to also include wall effects, using an additional potential that results from the assumption that,chain conformations have reflected random-walk statistics, as first advocated by Silberberg. Results for end-to-end vector and Rouse mode correlation functions of chains end-tethered to the surface compare well with those obtained from molecular dynamics simulations of a multichain system using the Kremer Grest bead spring model (KG MD). Even though the additional single-chain potential is parameter-free, we show that the accuracy of the model for surface chains is comparable to that of the Rouse model for bulk chains. An analytic dumbbell model accurately describes the longest Rouse mode correlation function of surface-tethered "mushroom" chains immersed in a polymer melt at low grafting density. In addition, we find that a perfectly smooth surface enhances the influence of hydrodynamic viscoelastic coupling on the center-of-mass motion near the surface.