The boundary-layer solutions for progressive edge waves on a uniformly sloping beach are derived. The Larangian mass transport in the cross-shore direction is found to be caused by the viscous effect and it changes direction within the boundary layer. For validation of the theoretical model, laboratory experiments are performed. The measured mass transports of mode 0 and 1 edge waves are in good agreement with the theory qualitatively but not quantitatively. The discrepancies appear to be caused by the failure of the theory near the shoreline, where the boundary layer is no longer thin. The inviscid Stokes drift caused by the nonlinear interactions of different edge-wave modes within the potential flow field is also investigated theoretically and verified by experiments. It is found that near-shore circulation cells can be formed by the nonlinear interactions between different progressive edge-wave modes.