We analyze the behavior of the linear phase of the Rayleigh-Taylor instability (RTI) in the presence of a foam. Such a problem may be relevant, for example, to some inertial confinement fusion (ICF) scenarios such as foams within the capsule or lining the inner hohlraum wall. The foam displays three different phases: by order of increasing stress, it is first elastic, then plastic, and then fractures. Only the elastic and plastic phases can be subject to a linear analysis of the instability. The growth rate is analytically computed in these two phases, in terms of the microstructure of the foam. In the first, elastic, phase, the RTI can be stabilized for some wavelengths. In this elastic phase, a homogenous foam model overestimates the growth because it ignores the elastic nature of the foam. Although this result is derived for a simplified foam model, it is likely valid for most of them. Besides the ICF context considered here, our results could be relevant to many fields of science.

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• Rayleigh-Taylor instability
• Foams