The characteristics of compressive shock wave propagation in the solid phase of a cellular material are studied in the present paper using a one-dimensional mass-spring model. The unique compressive stressstrain relation of a cellular material leads to several interesting observations on the characteristic of onedimensional stress wave transmission in a cellular material, which are important for understanding the blast and impact mitigation and attenuation through a cellular material. Generally, cellular material attenuates impact-or blast-induced loads by cell collapse mechanism at low impact velocities or low pulse pressure intensities when the stress transmission in a cellular material is limited by the plateau stress before the densification stage starts. This feature leads to wide applications of cellular materials in structural crashworthiness design where low speed impact is considered as potential survivable scenarios. However, scattered information has shown that stress enhancement in cellular material may occur when an intensive loading is applied, which, in contrast to the stress attenuation function of a cellular material, could produce more severe damage on the protected structures. This phenomenon is studied qualitatively in the present paper using a one-dimensional spring-mass model.