An annular elastic layer bonded between rigid plates and subjected to a compressive force normal to the layer is analyzed through a theoretical approach. On the basis of two kinematic assumptions, the governing equation for the mean pressure is established from the equilibrium equation, which is then solved by satisfying the stress boundary conditions. Through the obtained pressure expression, the compression stiffness of the bonded annular layer is derived in closed form and is very close to the finite element solution. The derived formula has no limitation on the Poisson's ratio and is more concise than the previous research. Through the asymptotic approach, the compression stiffness for the incompressible elastic layers is derived and is more accurate than the previous research obtained by directly neglecting the bulk compressibility. The stiffness reduction caused by the central hole is more prominent when the Poisson's ratio is close to 0.5.
