Solitary gravitational-sound waves are found to be supported by a collection of weakly-interacting massive particles (WIMPS). The necessary conditions, under which such a wave solution can be found, are completely determined. The wave solution, however, possesses weak singularities, which may potentially induce micro-instabilities that effectively dissipate the solitary wave. It is exactly due to the weak singularity that, no matter how small the wave amplitude is, the solution is always nonlinear in nature. If the effective dissipation can be modelled by a small effective viscosity, we find that the ideal solution remains valid in the large. In this situation, such solitary waves may serve to detect the physical parameters of WIMPS.