We study the linear diamagnetic response of a superconducting cylinder coated by a normal-metal layer due to the proximity effect using the clean limit quasiclassical Eilenberger equations. We compare the results for the susceptibility with those for a planar geometry. Interestingly, for R ~ d the cylinder exhibits a stronger overscreening of the magnetic field, i.e., at the interface to the superconductor it can be less than (−1 /2) of the applied field. Even for $${R\gg d}$$ , the diamagnetism can be increased as compared to the planar case, viz. the magnetic susceptibility 4πχ becomes smaller than −3/4. This behavior can be explained by an intriguing spatial oscillation of the magnetic field in the normal layer.