Cylindrically symmetric static solutions of the Einstein field equations   for elastic matter
  The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical solutions satisfying the dominant energy conditions. Furthermore, we show that the solutions can be matched at a finite radius to suitable $\Lambda$-vacuum exteriors given by the Linet-Tian spacetime. 
I. Brito, J. Carot, F. C. Mena, E.G.L.R. Vaz
gr-qc