  We investigate singularities of all parallel surfaces to a given regular
surface. In generic context, the types of singularities of parallel surfaces
are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal
butterfly and 3-dimensional $D_4^\pm$ singularities. We give criteria for these
singularities types in terms of differential geometry (Theorem 3.4 and 3.5).
