The authors deal with the flat light-like hypersurfaces in Lorentz-Minkowski 4-spaces, with specific attention to the study of their singilarities in which a classification has been given. They prove that the generic singularities are the suspended cuspidal edge, the suspended swallowtail, the suspended cuspidal cross cap and the \(A_{4}\)-type hypersurface singularity. The authors also observe that the suspended cuspidal cross cap does not appear as a generic singularity in the general case of light-like hypersurfaces. Finally, they end the paper by classifying generic singularities of flat space-like surfaces with partially parallel normal frame.