Summary: We present the solution of the linear elasticity equations governing the deformation of an elastic cylinder encased in a tube and subjected to uniform compression on the flat ends. The solutions for the stresses, strains, and displacements in the encased and compressed cylinder are all systematically determined from the basic solution of Lamé’s classical elasticity problem of the long tube subjected to internal and external pressures. We first derive the general elastostatic analysis for an encased hollow cylinder, stress-free at the cavity, and later particularize the solution to a solid cylindrical specimen. The effective modulus \(E_{eff}\) of the encased sample is found to be a function of the bulk modulus \(k\) and Poisson’s ratio \(\nu \) of the material. \(E_{eff}\) differs from \(k\) except for nearly incompressible materials, where \(E_{eff}\) approaches the bulk modulus value. In the incompressible case, we also show how a load applied on the cylinder’s flat ends is equivalent to, and can be replaced by, the same load acting on the curved surface. For compressible materials, a more general expression for \(E_{eff}\) is found that also accounts for the case deformation. These results explain the deformation of an axially compressed and encased cylindrical specimen tested in compressibility measuring devices. The present analysis thus contributes to a better understanding of how this device works and to the interpretation of measurements taken with it.