The Mueller matrix solution of vector radiative transfer for inhomogeneous random media of nonspherical scatterers under a pulse incidence is presented. Copolarized and cross-polarized bistatic scattering echoes can be numerically simulated. Temporally varying echoes well demonstrate volumetric and surface scattering mechanism and depict the inhomogeneous fraction profile of random scatterers. The effective height of inhomogeneous canopy inverted from the pulse echoes is discussed. Pulse echo patterns are also numerically simulated for polarimetric scattering from the model of random metal targets beneath the layered vegetation canopies.