Self-consistent steady-state plasma density profiles including the effects of the ponderomotive force for obliquely incident light have been obtained for the case of supersonic upstream flow velocity. The radial stability of these density profiles is studied in one-dimensional spherical geometry. Above a modest threshold laser field, these density profiles are found to be unstable and exhibit unsteady flow. The absorption for unstable profiles is found to vary markedly in time. Radiation and plasma waves can be trapped in density troughs which may be unstable to kink or sausage instabilities in two dimensions.