Abstract: The lowest-order nonstandard finite element schemes namely Morley, discontinuous Galerkin, and 𝐶0-interior penalty methods are presented for numerical discretization of the biharmonic wave equation with clamped boundary conditions in a unified framework. The regularity results we presented ensure the boundedness of various norms for the different derivatives of the continuous solution required in the error analysis. Stability results are obtained for both semidiscrete and fully discrete (implicit and explicit) schemes. A novel Ritz projection operator is used to obtain the error estimates. The expected convergence rates are confirmed by the numerical results, highlighting the versatility of the methods.