We have studied the interaction of soft-x-ray thermal radiation with foam-layered metal targets. X-ray radiation was produced by focusing a high-energy laser inside a small size hohlraum. An increment in shock pressure, up to a factor of approximately 4 for 50 mg/cm(3) foam density, was observed with the foam layer as compared to bare metal targets. This follows from the propagation of radiation-driven shock wave in the foam and the impedance mismatch at the foam-payload interface.