The paper is concerned with the equilibrium theory of elastic material
s with voids. An analogue of the Phragmen-Lindelof principle Sor a sem
i-infinite right cylinder composed of a homogeneous and anisotropic ma
terial is presented. The paper studies the asymptotic behaviour of sol
utions measured by the cross-sectional work function. The work-functio
n to within a rigid body displacement either decays faster than a cert
ain decreasing exponential function or grows faster than a growing exp
onential function. A uniqueness result is also derived.