  Eshelby's theory of inclusions has wide-reaching implications across the
mechanics of materials and structures including the theories of composites,
fracture, and plasticity. However, it does not include the effects of surface
stress, which has recently been shown to control many processes in soft
materials such as gels, elastomers and biological tissue. To extend Eshelby's
theory of inclusions to soft materials, we consider liquid inclusions within an
isotropic, compressible, linear-elastic solid. We solve for the displacement
and stress fields around individual stretched inclusions, accounting for the
bulk elasticity of the solid and the surface tension (\textit{i.e.} isotropic
strain-independent surface stress) of the solid-liquid interface. Surface
tension significantly alters the inclusion's shape and stiffness as well as its
near- and far-field stress fields. These phenomenon depend strongly on the
ratio of inclusion radius, $R$, to an elastocapillary length, $L$. Surface
tension is significant whenever inclusions are smaller than $100L$. While
Eshelby theory predicts that liquid inclusions generically reduce the stiffness
of an elastic solid, our results show that liquid inclusions can actually
stiffen a solid when $R<3L/2$. Intriguingly, surface tension cloaks the
far-field signature of liquid inclusions when $R=3L/2$. These results are have
far-reaching applications from measuring local stresses in biological tissue,
to determining the failure strength of soft composites.
