  We study theoretically the low-energy phonons and the static strain in
cylindrical core/shell nanowires (NWs). Assuming pseudomorphic growth,
isotropic media, and a force-free wire surface, we derive algebraic expressions
for the dispersion relations, the displacement fields, and the stress and
strain components from linear elasticity theory. Our results apply to NWs with
arbitrary radii and arbitrary elastic constants for both core and shell. The
expressions for the static strain are consistent with experiments, simulations,
and previous analytical investigations; those for phonons are consistent with
known results for homogeneous NWs. Among other things, we show that the
dispersion relations of the torsional, longitudinal, and flexural modes change
differently with the relative shell thickness, and we identify new terms in the
corresponding strain tensors that are absent for uncapped NWs. We illustrate
our results via the example of Ge/Si core/shell NWs and demonstrate that
shell-induced strain has large effects on the hole spectrum of these systems.
