A bifurcation analysis of a layered ductile structural element undergoing homogeneous, high-rate extension is presented. Formation of multiple strain localization sites provides a precursor to ductile fragmentation, and the objective of the analysis is to investigate the effect of an added surface layer on resistance of the structural element to fragmentation. The analysis shows that, in addition to dissipating plastic work, the outer layer can increase the total energy dissipation prior to fragmentation by increasing bifurcation strain. The analysis also shows that the strain hardening exponent of the outer layer plays an important role in increasing the bifurcation strain; higher values of hardening exponent result in higher bifurcation strain. Strength and density of the outer layer play a secondary role in increasing bifurcation strain. Once a material with a high hardening exponent is chosen for the outer material, its strength plays an important role in increasing the total dissipated energy. The analysis also reveals that, for certain combinations of strength and hardening exponent of the outer layer, the sandwich structure can dissipate more energy than a homogeneous core structure of the same total thickness and length. This is so even when the outer layer is weaker than the core. Energy dissipated per unit mass can be significantly improved by choosing a softer outer layer which displays high-strain hardening. Thus, the bifurcation analysis presented here provides a quantitative guideline for material selection in designing layered structures optimized for resistance to fragmentation.