The effect of the solidification transition on the edge phenomena of a two-dimensional (2D) electron system in a magnetic field is studied in the classical and quantum melting regimes. It is shown that in the pure solid system , instead of the conventional edge magnetoplasmons (EMP) which are observed in the liquid state, new magneto-Rayleigh waves (MRW) can propagate along the solid boundary and these have much lower frequencies: . If at a finite temperature the solidification of the edge is not completed due to the smooth density profile, the EMP and the new boundary displacement waves can propagate in a thin electron liquid strip surrounding the 2D solid. The properties of these waves are affected by the solid boundary which may provide an alternative approach for probing the Wigner transition.