The expansion problem of ideal gas and incompressible spherical monodisperse particles mixture in a closed shock tube has been posed and solved. An asymptotically accurate solution of the initial (self-similar) stage of expansion of the gas suspension with a fine powder fraction was obtained. For the nonequilibrium case of larger particles, the problem was solved numerically by the hybrid large-particle method of the second-order approximation in space and time. The double-speed splitting effects of the flow stratification and the interface both into the gas-phase contact and the porosity jump as well as the interaction of the reflected shock wave with them were revealed. For the late stage of expansion, the dynamics of the gas suspension layer was established to be similar to a nonlinear oscillatory dissipative system with attenuation and a drift of the split contact interfaces depending on the size of dispersed inclusions.