Abstract: Based on the theory of elasticity, an analytic expression is derived for the displacement of a cylindrical rubber bush mountings subjected to radial loading using Euler equations. The assumption of incompressibility is not adopted to evaluate the influence of Poisson’s ratio. And the radial stiffness for plane problem is deduced. The displacement’s increment after releasing the restrictions of both ends is derived using modified Bessel functions, and then, the exact radial stiffness of the bush with finite lengths is obtained according to superposition of displacements. It is shown that the influence of Poisson’s ratio on the radial stiffness is great when it is from 0.48 to 0.5. The calculated radial stiffness is consistent with that from the available experimental data.